System and method of monitoring, predicting and optimizing production yields in a liquid crystal display (LCD) manufacturing process

ABSTRACT

A system and method of monitoring LCD production yields, predicting the effects of different testing methodologies on LCD production yields, and optimizing production yields is provided that compares the effect of different testing methodologies on the yields at various stages in the LCD testing and assembly process. The present invention can also be used to predict the effect of different testing methodologies on user-defined parameters, such as profit.

[0001] This is a continuation of U.S. patent application Ser. No.10/355,059 filed Jan. 31, 2003.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] This invention relates to LCD manufacturing and, moreparticularly, to a system and method of monitoring LCD productionyields, predicting the effects of different testing methodologies on LCDproduction yields, and optimizing production yields.

[0004] 2. Background of the Related Art

[0005] Yield management is important in LCD manufacturing. In LCDmanufacturing, a single large plate of glass is divided into just ahandful of LCD panels. As consumer demand grows for larger and largerdisplays, substrates get larger and the number of LCD panels per glassplate decreases. Accordingly, production yields are critical in LCDmanufacturing.

[0006] The majority of the costs of an LCD panel comes frommanufacturing. As a result, profitability is closely linked to yieldrates. Any changes in yield rates will have a financial impact.

[0007] LCD panel production is a highly automated process involvingvarious manufacturing stages. Each manufacturing stage consists of manycomplex steps. For example, one stage of the process creates thethin-film transistor arrays on the glass substrate, which includesmultiple passes of thin film deposition, resist layers, exposure,development, etching and stripping. The opportunities for defects occurat nearly every step of every stage in the manufacturing process.

[0008] Defects take several different forms, and can generally bedivided into optical, mechanical and electrical defects. Some of thesedefects can be repaired, while others are permanent and may be severeenough to render the LCD panel unusable.

[0009] Optical defects are the most common defect. When this type ofdefect is present, a pixel is “stuck” in either a bright state, in whichthe pixel always transmits light, or a dark state, in which the pixelnever transmits light. The most common cause for this type of defect isan electrical problem, such as a short or an open circuit in the cell'stransistor or signal leads. Light or dark spots can also be caused byforeign particle contamination between the glass plates, or between theLCD panel and the backlight.

[0010] Another type of optical defect is non-uniformity, which can becaused by non-uniform cell gaps that result in varying thickness of theliquid crystal layer. Uniformity problems can also be caused by errorsin the rubbing process for liquid crystal alignment layers, inconsistentcolor filter thickness or incomplete removal of chemical residues.

[0011] Mechanical defects can include broken glass and broken electricalconnections. Broken electrical connections can arise from improperassembly, errors in alignment of the components and/or mishandling.

[0012] Some LCD manufacturers use testing and inspection equipment thatcan automatically evaluate panels at intermediate points in themanufacturing process. In some cases, the defects can be automaticallyrepaired. However, comprehensive testing in the LCD production processslows down production. In addition, there are capital and maintenancecosts associated with the test equipment. Accordingly, manufacturershave to balance the need for comprehensive and accurate testing againstthe need to avoid slowing production as much as possible.

SUMMARY OF THE INVENTION

[0013] An object of the invention is to solve at least the aboveproblems and/or disadvantages and to provide at least the advantagesdescribed hereinafter.

[0014] To achieve the objects, and in accordance with the purpose of theinvention, as embodied and broadly described herein, the presentinvention provides a system and method of monitoring LCD productionyields, predicting the effects of different testing methodologies on LCDproduction yields, and optimizing production yields by comparing theeffect of different testing methodologies on the yield at various stagesin the LCD testing and assembly process. The present invention can alsobe used to predict the effect of different testing methodologies onuser-defined parameters, such as profit.

[0015] In a preferred embodiment, the different testing methodologiesare evaluated using a common production run. This reduces the number ofLCD panels required to test the different methodologies, and alsoreduces the probability of LCD panels being sacrificed when an impropertesting methodology is applied.

[0016] Additional advantages, objects, and features of the inventionwill be set forth in part in the description which follows and in partwill become apparent to those having ordinary skill in the art uponexamination of the following or may be learned from practice of theinvention. The objects and advantages of the invention may be realizedand attained as particularly pointed out in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The invention will be described in detail with reference to thefollowing drawings in which like reference numerals refer to likeelements wherein:

[0018]FIG. 1A is a block diagram of the process flow for TFT-LCDfabrication, in accordance with the present invention;

[0019]FIG. 1B is a block diagram of one preferred embodiment of theprocessor of FIG. 1A;

[0020]FIG. 2 is a block diagram of the assembly stage 200 of the processflow shown in FIG. 1;

[0021]FIG. 3 is a plot showing the pixel voltage distribution when halfof the pixels of the TFT-array panel have positive pixel voltages andthe other half have negative pixel voltages, in accordance with thepresent invention;

[0022]FIG. 4 is a block diagram showing the layout of a typical glasssubstrate 400 used in TFT-LCD manufacturing;

[0023]FIG. 5 is a flow chart of a method of generating the distributionfunctions for normal pixels and defective pixels in an actual productionenvironment, in accordance with the present invention;

[0024]FIG. 6 is a defect sorting table, in accordance with the presentinvention;

[0025]FIG. 7 is a flow chart of a process for sorting defective pixelsdiscovered using the results of the array test stage, array repairstage, cell inspection stage and module inspection stage, in accordancewith the present invention;

[0026]FIG. 8 is a revised defect sorting table for primary-test-only atthe TFT-array test stage, in accordance with the present invention;

[0027]FIG. 9 is a revised defect sorting table for new-test-only at theTFT-array test stage, in accordance with the present invention;

[0028]FIG. 10 is a flow chart of a process for profit maximization forthe TFT-LCD production line can be achieved by optimization of thethresholding parameters, in accordance with the present invention;

[0029]FIG. 11 is a flow chart of a process for initial defect sorting,in accordance with the present invention;

[0030]FIG. 12 is a flow chart of a process for defect resorting for newscreen thresholding, in accordance with the present invention;

[0031] FIGS. 13A-13D illustrate a flow chart of a process for profitmaximization of new and primary test recipes, in accordance with thepresent invention;

[0032]FIG. 14 is a defect sorting table for tighter new thresholdingparameters for a new test recipe, in accordance with the presentinvention;

[0033]FIG. 15 is a defect sorting table for looser new thresholdingparameters for a new test recipe, in accordance with the presentinvention;

[0034]FIG. 16 is a revised defect sorting table, in conjunction with theinitial defect sorting of FIG. 11, for primary-test-only at theTFT-array test stage, in accordance with the present invention;

[0035]FIG. 17 is a plot showing an example of the distribution of normaland defective pixel voltages of a TFT-array panel, in accordance withthe present invention;

[0036]FIG. 18 is a plot showing the over-killed and under-killed defectsas the threshold parameters are scanned, in accordance with the presentinvention;

[0037]FIG. 19 is a plot showing the differential effect of changingthreshold parameters for under-killed defects, in accordance with thepresent invention;

[0038]FIG. 20 is a plot showing the differential effect of changingthreshold parameters on over-killed defects, in accordance with thepresent invention;

[0039]FIG. 21 is a plot showing the differential effect of changingthreshold parameters on cell and module yields, in accordance with thepresent invention;

[0040]FIG. 22 is a plot showing the differential effect of changingthreshold parameters on total monetary benefit, in accordance with thepresent invention;

[0041]FIG. 23 is a plot showing the under-killed defects for differentdefect density values, in accordance with the present invention;

[0042]FIG. 24 is a plot showing the differential effect of changingthreshold parameters on the total monetary benefit, in accordance withthe present invention; and

[0043]FIG. 25 is a plot showing how the profit improvement increaseswith increasing defect density, in accordance with the presentinvention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0044] I. Thin-Film Transistor (TFT) Liquid Crystal Display (LCD)Fabrication

[0045]FIG. 1A is a block diagram of the process flow for TFT-LCDfabrication. The fabrication process can be divided into two stages, anarray panel fabrication stage 100, in which the thin-film transistor(TFT) array panels are fabricated on a substrate, and a test andassembly stage 200, in which the TFT array panels are tested and thedisplays are assembled.

[0046] In the array panel fabrication stage, the glass substrate onwhich the TFT array panels are fabricated is cleaned at step 102. Steps104-110 represent well known process steps for forming TFT array panelson a glass substrate. They consist of a thin film deposition step 104, aphotoresist patterning step 106, and etching step 108 and a photoresiststripping and cleaning step 110. Steps 104-110 are repeated for eachpatterned thin film layer that is deposited on the glass substrate.

[0047] Multiple TFT array panels are typically fabricated on each glasssubstrate, which are also referred to as TFT-array base plates. Adisplay unit, such as an LCD display, utilizes one TFT array panel.

[0048] Once the TFT array panels are fabricated on the glass substrate,the TFT array panels proceed to the test and assembly stage 200, duringwhich the TFT array panels are tested, the liquid crystal (LC) cells areassembled and separated, and the electrical connections are made to theliquid crystal cells to yield the liquid crystal modules that willultimately be used in the LCDs. The assembly stage consists of varioussubstages, including an array test stage 202, an array repair stage 204,a cell assembly stage 206, a cell inspection stage 208, a moduleassembly stage 210 and a module inspection stage 212. The assembly stage200 may also optionally include a cell repair stage 214 and a modulerepair stage 216.

[0049] In the array test stage 202, each TFT array panel is tested bydriving the panel with a test signal, which will be explained in moredetail below. TFT array panels that are determined to be bad (e.g.,defective) are sent to the array repair stage 204. The panels that aredetermined to be good are sent to the cell assembly stage 206. In thearray repair stage 204, the bad panels that can be repaired are repairedusing techniques known in the art, and the repaired panels are then sentto the cell assembly stage 206.

[0050] In the cell assembly stage 206, the LC cells are assembled bylaminating front and rear glass plates to the TFT array panels andinjecting liquid crystal material between the front and rear glassplates using techniques known in the art. In addition, the individual LCcells are separated from each other at this stage by dicing the TFTarray base plate (glass substrate).

[0051] The assembled and separated LC cells are then sent to the cellinspection stage 208, where they are inspected for defects. LC cellsthat are determined to be damaged can be sent to an optional cell repairstage 214. The LC cells that are determined to be good LC cells, and therepaired LC cells, if the optional cell repair stage 214 is implemented,are then sent to the module assembly stage 210.

[0052] In the module assembly stage 210, the required electricalconnections are made to the LC cells to yield the LCD modules that willultimately be used in LCDs. The LCD modules then proceed to the moduleinspection stage 212, where they are tested using techniques known inthe art. An optional module repair stage 216 can be used to repair LCDmodules that are deemed to be defective at the module inspection stage212.

[0053] A processor 220 sends and receives data to/from the test andassembly stage 200. In a preferred embodiment, shown in FIG. 1B, theprocessor 220 includes a comparison unit 222 and an estimating unit 224.The comparison unit 222 compares the inputs and outputs of the varioussubstages in the test and assembly stage 200 for different manufacturingsetups. The estimating unit 224 receives comparison data from thecomparison unit 222, and estimates the effect that a change in themanufacturing setup has on a desired parameter, such as profit. Theestimating unit 224 utilizes methodologies that will be described below.The estimate data produced by the estimating unit 224 may be used tooptimize the manufacturing setup used by the test and assembly stage200.

[0054] The processor 220 of the present invention is preferablyimplemented on a server may be implemented on a programmed generalpurpose computer, a special purpose computer, a programmedmicroprocessor or microcontroller and peripheral integrated circuitelements, an ASIC or other integrated circuit, a hardwired electronic orlogic circuit such as a discrete element circuit, a programmable logicdevice such as a FPGA, PLD, PLA, or PAL, or the like. In general, anydevice on which a finite state machine capable of implementing theprocess steps and routines discussed below can be used to implement theprocessor 220.

[0055] II. Profit Model for TFT-LCD Fabrication

[0056] A profit model for TFT-LCD fabrication, in accordance with oneembodiment of the present invention, will be described with reference toFIG. 2, which is a block diagram of the assembly stage 200 of theprocess flow shown in FIG. 1.

[0057] The variables used to describe the main process stages of FIG. 2are defined as follows:

[0058] I_(A)=Number of input panels to array test stage 202;

[0059] I_(AR)=Number of input panels to array repair stage 204;

[0060] I_(C) Number of input panels to cell inspection stage 208;

[0061] I_(M) Number of input panels to module inspection stage 212;

[0062] O_(ATG)=Number of passed panels at array test stage 202;

[0063] O_(ATB)=Number of irreparably bad panels at array test stage 202;

[0064] O_(ATR)=Number of reparable panels at array test stage 202, whichis the same as I_(AR);

[0065] O_(ARG)=Number of passed panels at array repair stage 204;

[0066] O_(ARB)=Number of bad panels at array repair stage 204;

[0067] O_(CG)=Number of passed panels at cell inspection stage 208;

[0068] O_(CB)=Number of irreparably bad panels at cell inspection stage208;

[0069] O_(MG)=Number of passed panels at module inspection stage 212;and

[0070] O_(MB)=Number of irreparably bad panels at module inspectionstage 212.

[0071] For the optional production flow stages 214 and 216, theadditional variables used are defined as follows:

[0072] O_(CIR)=Number of reparable panels at cell inspection stage 208;

[0073] O_(MIR)=Number of reparable panels at module inspection stage212;

[0074] O_(CRG)=Number of passed panels at cell repair stage 214;

[0075] O_(MRG)=Number of passed panels at module repair stage 216;

[0076] O_(CRB)=Number of bad panels at cell repair stage 214; and

[0077] O_(MRB)=Number of bad panels at module repair stage 216.

[0078] A model that describes the relationship between profits andvariations in yields at cell and module inspections will now bedescribed. Certain cost variables will be used as follows:

[0079] C_(A)=Cost to make a TFT panel;

[0080] C_(T)=Cost to test a TFT panel;

[0081] C_(R)=Cost to repair a TFT panel;

[0082] C_(C)=Cost of cell assembly for a TFT panel;

[0083] C_(CI)=Cost of cell inspection for a TFT panel;

[0084] C_(M)=Cost of module assembly for a TFT panel; and

[0085] C_(MI)=Cost of module inspection for a TFT panel.

[0086] In order to have an initial reference for the evaluation ofchanges in the manufacturing parameters used in the testing, inspection,or assembly stages, a current manufacturing setup is called a “primarymanufacturing setup”, and the results obtained with the primarymanufacturing setup are referred to as “primary results.”

[0087] The cost analysis is done in connection with the assembly stage200 of the process flow, without the optional cell repair stage 214 andmodule repair stage 216. This assumes that there is no difference incosts and output quantities between the primary manufacturing setup anda proposed new manufacturing setup. The cost to manufacture a TFT-LCDpanel using the primary setup, COST_(PRIME), can be expressed asfollows:

COST_(PRIME)=Array manufacturing cost+Array test cost+Array repaircost+Cell assembly cost+Cell inspection cost+Module assembly cost+Moduleinspection cost.  (1)

[0088] One can obtain the expressions for the cost values as follows:

Array manufacturing cost=I _(A) C _(A)  (2)

Array test cost=I _(A) C _(T)  (3)

Array repair cost=I _(AR) C _(T)  (4)

Cell assembly cost=I_(C) C _(C)  (5)

Cell inspection cost=I _(C) C _(CI)  (6)

Module assembly cost=I _(M) C _(M)  (7)

Module inspection cost=I _(M) C _(MI)  (8)

[0089] The yields at each stage are defined as follows:

Yield of array test (Y _(AT))=O _(ATG) /I _(A)  (9)

Yield of array repair (Y _(AR))=O _(ARG) /I _(AR)  (10)

Yield of cell inspection (Y _(C))=O _(CG) /I _(C)  (11)

Yield of module inspection (Y _(M))=O _(MG) /I _(M)  (12)

[0090] Since I_(M)=O_(CG) without the optional cell repair and modulerepair stages 214 and 216, Equation (11) can be written as:

I _(M) =Y _(C) I _(C)  (13)

[0091] From Equations (1), (2)-(8), and (13) one obtains:

COST _(PRIME) =I _(A) C _(A) +I _(A) C _(T) +I _(AR) C _(T) +I _(C) C_(C) +I _(C) C _(CI) +Y _(C) I _(C) C _(M) +Y _(C) I _(C) C _(MI)  (14)

[0092] The value of the final TFT-LCD module output, in the case of theprimary manufacturing setup without the optional cell repair and modulerepair stages 214 and 216, can be expressed as follows:

PRODUCT _(PRIME) =O _(MG) P _(VALUE),  (15)

[0093] where P_(VALUE) is the value of a TFT-LCD module fabricated usingthe primary manufacturing setup. From Equations (12), (13), and (14),one obtains:

PRODUCT _(PRIME) =Y _(M) Y _(C) I _(C) P _(VALUE)  (16)

[0094] When a new manufacturing setup is used in the array test stage202, cell inspection stage 206, module inspection stage 212, cellassembly stage 206, and/or module assembly stage 210, one can expect tohave new values represented by the following variables:

[0095] I′_(AR)=New number of input panels to array repair;

[0096] I′_(C)=New number of input panels to cell inspection;

[0097] I′_(M)=New number of input panels to module inspection;

[0098] O′_(ATG)=New number of passed panels at array test;

[0099] O′_(ATB)=New number of irreparably bad panels at array test;

[0100] O′_(ATR)=New number of reparable panels at array test, which isthe same as I′_(AR);

[0101] O′_(ARG)=New number of passed panels at array repair;

[0102] O′_(ARB)=New number of bad panels at array repair;

[0103] O′_(CG)=New number of passed panels at cell inspection, which issame as I′_(M);

[0104] O′_(CB)=Number of bad panels at cell inspection;

[0105] O′_(MG)=New number of passed panels at module inspection;

[0106] O′_(MB)=New number of bad panels at module inspection;

[0107] Y′_(AT)=New yield of array test;

[0108] Y′_(AR)=New yield of array repair;

[0109] Y′_(C)=New yield of cell inspection; and

[0110] Y∝_(M)=New yield of module inspection.

[0111] One can then obtain a new set of expressions for the newmanufacturing setup, without the optional cell repair and module repairstages 214 and 216, as follows:

COST _(NEW) =I _(A) C _(A) +I _(A) C _(T) +I′ _(AR) C _(R) +I′ _(C) C_(C) +I′ _(C) C _(CI) +Y′ _(C) I′ _(C) C _(M) +Y′ _(C) I′ _(C) C_(MI)  (17)

PRODUCT _(NEW) =Y′ _(M) Y′ _(C) I′ _(C) P′ _(VALUE),  (18)

[0112] where P′_(VALUE) is the value of the TFT-LCD module fabricatedwith the new manufacturing setup.

[0113] The profit increase (or deficit decrease), P, that results fromthe new manufacturing setup is obtained as follows:

P=COST _(PRIME) −COST _(NEW) +PRODUCT _(NEW) −PRODUCT _(PRIME)  (19)

[0114] From Equations (14), (16), (17), (18), and (19) one obtains thefollowing expression for P:

P=(I_(AR) −I′ _(AR))C _(R)+(I_(C) −I′ _(C))C _(C)+(I _(C−I′) _(C))C_(CI) +Y _(C) I _(C) C _(M) +Y _(C) I _(C) C _(MI) −Y′I′ _(C) C _(M) −Y′_(C) I′ _(C) C _(MI) +Y′ _(M) Y′ _(C) I′ _(C) P′ _(VALUE) −Y _(M) Y _(C)I _(C) P _(VALUE)   (20)

[0115] During regular production of a TFT-LCD, one can assume thatO_(ATB)+O_(ARB)≅O′_(ATB)+O′_(ARB), because a bad panel usually getscarried to the next process stage, as the individual panels have not yetbeen separated from each other and are all on a common TFT-array baseplate. If this assumption is valid, then with

I _(C) =I _(A)−(O _(ATB) +O _(ARB)), and  (21)

I′ _(C) =I _(A)−(O′ _(ATB) +O′ _(ARB)),  (22)

[0116] one obtains:

I _(C) ≅I′ _(C)  (23)

[0117] Using Equation (23) in Equation (20), one obtains

P≅(I _(AR) −I′ _(AR))C _(R)+(Y _(C) −Y′ _(C))I _(C)(C _(M) +C _(MI))+(Y′_(M) Y′ _(C) P′ _(VALUE) −Y _(M) Y _(C) P _(VALUE))I _(C)  (24)

[0118] Since the value of a TFT-LCD module is irrelevant to themanufacturing setup, one obtains:

P _(VALUE) =P′ _(VALUE)  (25)

[0119] Thus, with Equation (25), Equation (24) can be further simplifiedas:

P≅(I _(AR) −I′ _(AR))C _(R)+(Y _(C) −Y′ _(C))I _(C)(C _(M) +C _(MI))+(Y′_(M) Y′ _(C) −Y _(M) Y _(C))P _(VALUE) I _(C)  (26)

[0120] Accordingly, Equation (26) can be used to calculate the profitincrease or decrease as a result of the yield variation that occurs dueto a new manufacturing setup.

[0121] One can use the relationships described above to evaluate theprofits and the production quantities needed to achieve a break-evenpoint in TFT-LCD manufacturing. This type of cost analysis is done basedon the assumption that no TFT array panels are discarded as bad panelsduring TFT array process. The cost of TFT-LCD panel (COST) can beexpressed as follows:

COST=Array manufacturing cost+Array test cost+Array repair cost+Cellassembly cost+Cell inspection cost+Module assembly cost+Moduleinspection cost+Packaging cost+Storage and transportation cost+Otherfixed cost.  (27)

[0122] One can obtain additional expressions for the cost values asfollows:

Packaging cost=I _(M) C _(P); and  (28)

Storage and transportation cost=I _(M) C _(S),  (29)

[0123] where C_(P) and C_(S) are the unit packaging andstorage/transportation cost, respectively.

[0124] From Equations (2)-(8), (13), (27), (28), and (29) one obtains:

COST=I _(A) C _(A) +I _(A) C _(T) +I _(AR) C _(R) +I _(C) C _(C) +I _(C)C _(CI) +Y _(C) I _(C)(C _(M) +C _(MI) +C _(P) +C _(S))+C _(F),  (30)

[0125] where C_(F) is other fixed costs. The value of the final output,without the optional cell and module repair stages 214 and 216, can beexpressed as follows:

PRODUCT=O _(MG) D _(SALE),  (31)

[0126] where D_(SALE) is the sales price of a TFT-LCD product unit.

[0127] From Equations (12), (13), and (31), one obtains:

PRODUCT=Y _(M) Y _(C) I _(C) D _(SALE).  (32)

[0128] Then, the profit (PT) is obtained by:

PT=PRODUCT−COST.  (33)

[0129] From Equations (30), (32), and (33), one obtains:

PT=Y _(M) Y _(C) I _(C) D _(SALE)−(I _(A) C _(A) +I _(A) C _(T) +I _(AR)C _(R) +I _(C) C _(C) +I _(C) C _(CI) +Y _(C) I _(C)(C _(M) +C _(MI) +C_(P) +C _(S))+C _(F)).  (34)

[0130] Using Equation (21) in Equation (34), one obtains:

PT=Y _(M) Y _(C)(I _(A) −O _(ATB) −O _(ARB))D _(SALE)(I _(A) C _(A) +I_(A) C _(T) +I _(AR) C _(R) +C _(F)+(I _(A) −O _(ATB) −O _(ARB))(C _(C)−C _(CI) −Y _(C) C _(M) +Y _(C) C _(MI) Y _(c) C _(P) Y _(C) C_(S))).  (35)

[0131] If one defines Y_(T) as:

Y _(T)≅(O_(ATB) +O _(ARB))/I _(A),  (36)

[0132] then Equation (35) becomes:

PT=Y _(M) Y _(C) I _(A)(1−Y _(T))D _(SALE)−(I_(A)(C _(A) C _(T))+I_(AR)C _(R) +C _(F) +I _(A)(1−^(Y) _(T))(C _(C) +C _(CI) +Y _(C)(C _(M) +C_(MI) +C _(P) +C _(S)))).  (37)

[0133] I_(A) for the break-even point where PT is zero (I_(A−EVEN))becomes:

I _(A-EVEN)=(I _(AR) C _(R) +C _(F))/(Y _(M) Y _(C)(1−Y _(T))D_(SALE)−(C _(A) +C _(T)+(1−Y _(T))(C _(C) +C _(CI) +Y _(C)(C _(M) +C_(MI) +C _(P) +C _(S))))).  (38)

[0134] In normal production, one can assume:

O _(AR<<I) _(A)  (39)

[0135] Thus, with Equation (9), one obtains:

I _(AR) =O _(ATR) =I _(A) −O _(ATB) −O _(ATG) ≅I _(A) −O _(ATG) =I_(A)(1−Y_(AT)).  (40)

[0136] From Equations (37) and (40), one obtains:

PT≅Y _(M) Y _(C) I _(A)(1−Y _(T))D _(SALE)−(C _(F) +I _(A)(C _(A) +C_(T)+(1−Y _(AT))C _(R)+(1−Y _(T))(C _(C) +C _(CI) +Y _(C)(C _(M) +C_(MI) +C _(P) +C _(S))))).  (41)

[0137] I_(A-EVEN) is again obtained for I_(A), making PT=0 in Equation(41), as follows:

I _(A-EVEN) ≅C _(F)/(Y _(M) Y _(C)(1−Y _(T))D _(SALE)−(C _(A) +C_(T)+(1−Y _(AT))C _(R)+(1−Y _(T))(C _(C) +C _(CI) +Y _(C)(C _(M) +C_(MI) +C _(P) +C _(S))))).  (42)

[0138] Accordingly, the profit and the production quantities needed forbreak-even can be derived from yield numbers, cost numbers and salesprice.

[0139] The profit model described above is applicable to a productionline model that does not utilize the cell and module repair stages 214and 216. However, it should be appreciated that the profit modeldescribed above can be adapted for a production line model that doesutilize the optional cell and model repair stages 214 and 216, whilestill falling within the scope of the present invention. Further, if theoptional cell and module repair stages 214 and 216 are used, but thecell and module repair rates are so low as to not make a significantcontribution to the yield rates, then the above-described profit modelmay be applied.

[0140] III. Identifying Defects During TFT-Array Panel Testing

[0141] Each TFT-array panel is tested in the array test stage 202 usingarray testing equipment known in the art. When each TFT-array panel istested by the array testing equipment, the TFT-array panel is driven byelectrical signals and the storage capacitor of each pixel goes throughelectrical charging and discharging operations in order to achievecertain target voltage signals. The sensor of the array test equipmentmeasures the pixel voltage on the storage capacitor of every pixel ofthe TFT-array panel. If a pixel has a defect, then the pixel voltage ofthe defected pixel is different from the pixel voltage of the normalpixels. The difference between the defected pixel voltage and the normalpixel voltage is called a “defect signal.”

[0142]FIG. 3 is a plot showing the pixel voltage distribution when halfof the pixels of the TFT-array panel have positive pixel voltages andthe other half have negative pixel voltages. These distributions can berepresented by a statistical distribution function because of the largenumber of pixels in each TFT-array panel, and because of the sensor'sstatistical behavior. The distribution function for normal positivepixel voltages 310 is well represented by a normal distribution functionas follows:

Θ_(p) =N _(P)exp [−(v−V _(P))²/(2σ_(P) ²)]/{square root}{square rootover (2πσ_(P) ²)},  (43)

[0143] where Θ_(p) represents the distribution function for normalpositive pixel voltages, N_(P) is the total number of pixels havingnormal positive pixel voltages, v is a pixel voltage variable, V_(P) isa mean value and σ_(P) is a standard deviation of the normaldistribution function for positive pixel voltages.

[0144] N_(P) can be obtained by subtracting the number of defectivepixels having positive pixel voltages from the total number of pixelshaving positive pixel voltages, and can be approximated to be the totalnumber of pixels having positive pixel voltages because the number ofdefective pixels having positive pixel voltages is far lower than thenumber of normal pixels having positive pixel voltages.

[0145] The distribution function for normal negative pixel voltages 320is similarly well represented by a normal distribution function asfollows:

Θn=N _(N)exp [−(v−V _(N))²/(2σ_(N) ²)]/{square root over (2πσ_(N)²)},  (44)

[0146] where Θ_(n) represents the distribution function for normalnegative pixel voltages, N_(N) is a total number of pixels having normalnegative pixel voltage, and V_(N) is a mean value and σ_(N) is astandard deviation of normal distribution function for negative pixelvoltages.

[0147] N_(N) can be obtained by subtracting the number of defectivepixels having negative pixel voltages from the total number of pixelshaving negative pixel voltages, and can be approximated to be the totalnumber of pixels having negative pixel voltages because the number ofdefective pixels having negative pixel voltages is far lower than thenumber of normal pixels having negative pixel voltages. The values ofV_(P), σ_(P), V_(N), and σ_(N) can be typically obtained from the arraytesting equipment.

[0148] The plot of FIG. 3 also shows the defective pixel voltagedistributions 330 (θph), 340 (θpl), 350 (θnh), and 360 (θnl). θph andθpl represent the defective pixel voltage distributions in response todriving signals that produce positive polarity pixel voltages. θnh andθnl represent defective pixel voltage distributions in response todriving signals that produce negative polarity pixel voltages.

[0149] The array testing equipment uses thresholding parameters ofVthi+, Vtlo+, Vthi−, and Vtlo− to detect the defective pixels. Pixelsdriven to have positive pixel voltages are reported as defective whentheir pixel voltages fall outside of the positive threshold regionbetween Vthi+ and Vtlo+. Pixels driven to have negative pixel voltagesare reported as defective when their pixel voltages fall outside of thenegative threshold region between Vthi− and Vtlo−.

[0150] Under-Killed and Over-Killed Defects

[0151] If a normal pixel exhibits a pixel voltage that is outside of thethreshold region, then the normal pixel is wrongly classified as adefective pixel. This erroneous classification is called an “over-killeddefect.” If a defective pixel exhibits a pixel voltage that is inside ofthe threshold region, then the defective pixel is wrongly characterizedas a normal pixel. This erroneous classification is called an“under-killed defect.”

[0152] Under-killed defects lower the yields at the cell inspectionstage 208 (Y_(C)) and/or the yields at the module inspection stage 212(Y_(M)). Over-killed defects lower the productivity of the array repairequipment used in the array repair stage 204. Therefore it is veryimportant to set the right values for the thresholding parameters, inorder to maximize profit or minimize the loss of product fabrication.

[0153] IV. Effects of Bad Cells/Modules on the Number of Under-killedDefects

[0154]FIG. 4 is a block diagram showing the layout of a typical glasssubstrate 400 used in TFT-LCD manufacturing. The glass substrate 400generally consists of multiple TFT-array panels 400 a-400 i, and eachpanel is used for a display unit assembly. If the display is classifiedas a bad unit when it has just a single defect, then the number of baddisplays is determined as described below.

[0155] When there is only one defect in the glass substrate 400, the onedefect can fall on any one of the n panels. Thus, one defect causes onebad display unit. Accordingly, the total number of bad panels in thecase of single defect in the glass substrate 400 (N_(BAD−PANEL1)) is:

N _(BAD−PANEL1)=1.  (45)

[0156] When there is second defect in the glass substrate 400, thesecond defect can fall on any one of the n panels. If the second defectfalls on the same panel that the first defect falls on, then the seconddefect does not result in a new bad panel. However, the second defectwill cause a new bad panel if it falls on one of the other panels. Thusthe probability of causing another bad panel by a second defect (P₂)becomes:

P ₂=(n−1)/n.  (46)

[0157] Thus, from Equations (45) and (46), the total number of badpanels in the case of two defects in the glass substrate(N_(BAD−PANEL2)) is:

N _(BAD−PANEL2) =N _(BAD−PANEL1) +P ₂=1+(n−1)/n.  (47)

[0158] When there is third defect in the glass substrate 400, the thirddefect can fall on any one of the n panels. If the third defect falls ona panel that already has any number of defects, then the third defectdoes not result in a new bad panel. However, the third defect will causea new bad panel if it falls on a panel that has no defect. Thus, theprobability of causing another bad panel by the third defect (P₃) is:

P ₃ =P _(DOUBLE)(n−1)/n+(1−P _(DOUBLE))(n−2)/n,  (48)

[0159] where P_(DOUBLE) is the probability of having two defects in thesame panel, and is given by:

P _(DOUBLE) =n(1/n)(1/n)=1/n.  (49)

[0160] Thus, P₃ becomes:

P ₃=(1/n)(n−1)/n+(1−1/n)(n−2)/n=(n−1)² /n ².  (50)

[0161] Thus, from Eqs. (47) and (50), the total number of bad panels inthe case of three defects present in the glass substrate 400(N_(BAD−PANEL3)) is:

N _(BAD−PANEL3) =N _(BAD−PANEL2) +P ₃=1+(n−1)/n+(n−1)² /n ².  (51)

[0162] When there is fourth defect in the glass substrate 400, thefourth defect can fall on any one of the n panels. If the fourth defectfalls on a panel that already has any number of defects, then the fourthdefect does not result in a new bad panel. However, the fourth defectresults in a new bad panel if it falls on a panel that has no defect.Thus, the probability of causing another bad panel by the fourth defect(P₄) is:

P ₄ =P _(TRIPLE)(n−1)/n+P _(DOUBLE−SINGLE)(n−2)/n+(1−P _(TRIPLE) −P_(DOUBLE−SINGLE))(n−3)/n,  (52)

[0163] where P_(TRIPLE) is the probability of having three defects inthe same panel, and is given by:

P _(TRIPLE) =n(1/n)(1/n)(1/n)=1/n ²,  (53)

[0164] and P_(DOUBLE−SINGLE) is the probability of having two defects inthe same panel and one defect in different pane, and is given by:

P _(DOUBLE−SINGLE) =n(1/n)(1/n)(n−1)/n=(n−1)/n ².  (54)

[0165] Thus, P₄ becomes:

P₄=(1/n ²)(n−1)/n+((n−1)/n ²)(n−2)/n+(1−1/n ²−(n−1)/n ²)(n−3)/n=(n−1)/n³+(n−1)(n−2)/n ³+(1−1/n ²−(n−1)/n ²)(n−3)/n=(n−1+(n−1)(n−2)+(n²−1−(n−1))(n−3))/n ³=(n−1+(n−1)(n−2)+n(n−1)(n−3))/n³=(n−1)(1+n−2+n(n−3))/n ³=(n−1)(n ²−2n−1)/n³.   (55)

[0166] Thus, from Equations (51) and (55), the total number of badpanels in the case of four defects present in the glass substrate 400(N_(BAD−PANEL4)) is:

N _(BAD-PANEL4) =N _(BAD-PANEL3) +P ₄=1+(n−1)/n+(n−1)² /n ²+(n−1)(n²−2n−1)/n ³.  (56)

[0167] In a normal production line, it is very rare that the number ofdefects per glass substrate exceeds four. If the under-killed defects ofthe TFT-array test equipment are the dominant cause of bad panels atcell and module inspections, one can assume that the number of cell andmodule defects is proportional to the number of under-killed defects asfollows:

N _(CELL-DEFECT) =αU; and  (57)

N _(MODULE-DEFECT) =βU,  (58)

[0168] where α and β are the proportionality constants for cell andmodule defects, respectively. Then, from Equations (45), (47), (51),(56), (57), and (58), one can obtain:

N _(BAD-CELL)=α;  (59)

N _(BAD-CELL2)=α(1+(n−1)/n);  (60)

N _(BAD-CELL3)=α(1+(n−1)/n+(n−1)² /n ²);  (61)

N _(BAD-CELL4)=α(1+(n−1)/n+(n−1)² /n ²+(n−1)(n ²−2n−1)/n ³);  (62)

N _(BAD-MODULE1)=β;  (63).

N _(BAD-MODULE2)=β(1+(n−1)/n);  (64)

N _(BAD-MODULE3)=β(1+(n−1)/n+(n−1)² /n ²); and  (65)

N _(BAD-MODULE4)=β(1+(n−1)/n+(n−1)² /n ²+(n−1)(n ²−2n−1)/n ³),  (66)

[0169] where N_(BAD-CELL) and N_(BAD-MODULE) are the number of bad cellsand modules, respectively.

[0170] If the number of under-kill defects per glass substrate does notexceed approximately four, and the number of panels per glass substrate(n) is significantly larger than 1, then one obtains:

N_(BAD-CELL1)=α;  (67)

N _(BAD-CELL2)≅2α;  (68)

N _(BAD-CELL3)≅3α;  (69)

N _(BAD-CELL4)≅4α;  (70)

N_(BAD-MODULE1=β;)  (71)

N _(BAD-MODULE2)≅2β;  (72)

N _(BAD-MODULE3)≅3β; and  (73)

N _(BAD-MODULE4)≅4β.  (74)

[0171] Equations (67) to (70) can be summarized as:

N _(BAD-CELL) ≅Uα,  (75)

[0172] and Equations (71) to (74) can be summarized as:

N _(BAD-MODULE) ≅Uβ.  (76)

[0173] V. Test Recipes

[0174] Ideally, the array testing equipment is supposed to identify allthe defective pixels in the TFT-array panel without misclassifyingnormal pixels as a defective pixels. However, in reality, the arraytesting equipment may miss actual defective pixels (under-killeddefects) and wrongly classify normal pixels as defective pixels(over-killed defects).

[0175] The phrase “test recipe” is used herein to refer to the testingparameters used by the array testing equipment, e.g., the amplitude,timing and shape of the pixel driving signal, and the thresholdingparameters used to classify pixels as normal or defective. A currentlyused recipe is referred to herein as a “primary test recipe”, and itsresult is called a “primary test result”. A proposed new test recipe isreferred to herein as a “new test recipe”, and its result is called a“new test result.”

[0176] A new test recipe is classified herein as either a “newthresholding test recipe” or a “new distribution function test recipe.”A new thresholding recipe is one that only changes the thresholdingparameters, without affecting the voltage distribution functions of thenormal and defective pixels. A new distribution function recipe is onethat changes the voltage distribution functions of the normal and/ordefective pixels.

[0177] VI. Effects of Under-Killed Defects on Profits

[0178] When a new test recipe is used in the array testing equipment,the numbers of under-killed and over-killed defects may change fromthose of the primary test recipe. A method for determining the effectsthat under-killed defects have on the yields and profits in TFT-LCDmanufacturing will now be described. The method described below assumesthat the optional cell repair and module repair stages 214 and 216 arenot implemented.

[0179] If under-killed defects are the dominant cause of bad panels atthe cell inspection stage 208 (O_(CB) in FIG. 2), then one can assumethat the rate of bad panels at the cell inspection stage 208 isproportional to the number of under-killed defects (refer to Equation(75)), and obtain the following expression:

O _(CB) /I _(C) :U=O′ _(CB) /I′ _(C) :U′,  (77)

[0180] where U is the number of under-killed defects for the primarytest recipe and U′is the number of under-killed defects for the new testrecipe. Then, one obtains:

O′ _(CB) /I _(C) =O _(CB) U′/(I _(C) U).  (78)

[0181] Without the optional cell and module repair stages 214 and 216,

O _(CB) =I _(C) −O _(CG).  (79)

[0182] Thus, with Equation (78), one obtains:

(I′ _(C) −O′ _(CG))/I′ _(C)=(I _(C) −O _(CG))U′/(I _(C) U),  (80)

[0183] which becomes:

1−O′ _(CG) /I′ _(C)=(1−O _(CG) /I _(C))U′/U.  (81)

[0184] From Equations (11) and (81), one obtains:

Y′ _(C)=1−(1−Y _(C))U′/U.  (82)

[0185] Then, the improvement of the yield at the cell inspection stage208 (E_(YC)) can be expressed as:

E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y _(C))(1−U′/U).  (83)

[0186] If the under-killed defects are the dominant cause of the badpanels at the module inspection stage 212 (OMB in FIG. 2), then one canalso assume that the rate of bad panels at the module inspection stage212 is proportional to the number of under-killed defects (refer toEquation (76)), and obtain following expression:

O _(MB) /I _(M) :U=O′ _(MB) /I′ _(M) :U′.  (84)

[0187] Then, one obtains:

O′ _(MB) /I′ _(M) =O _(MB) U′/(I _(M) U).  (85)

[0188] Since O_(MB)=I_(M)−O_(MG) without the optional cell and modulerepair stages 214 and 216, with Equation (85), one obtains:

(I′ _(M) −O′ _(MG))/I′ _(M)=(I _(M) −O _(MG))U′/(I _(M) U),  (86)

[0189] which becomes: 1−O′ _(MG) /I′ _(M)=(1−O _(MG) /I _(M))U′/U.  (87)

[0190] From Equations (12) and (87), one obtains:

Y′ _(M)=1−(1−Y _(M))U′/U.  (88)

[0191] Then, the yield improvement at the module inspection stage 212(E_(YM)) can be expressed as:

E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y _(M))(1−U′/U).  (89)

[0192] From Equations (82), (88), and (26), one obtains:

P≅(I _(AR) −I′ _(AR))C _(R)+(Y _(C)−(1−(1−Y _(C))U′/U))I _(C)(C _(M) +C_(MI))+((1−(1−Y _(M))U′/U)(1−(1−Y _(C))U′/U)−Y _(M) Y _(C))P _(VALUE) I_(C).  (90)

[0193] The effect of a new test recipe on the over-killed panels, ΔQ,and on the under-killed panels, ΔU, can be expressed as:

ΔQ=Q−Q′=γ(Q−Q′)=γΔQ; and  (91)

ΔU=U−U′−γ(U−U′)=γΔU,  (92)

[0194] where Q and Q′ are the numbers of over-killed defects for theprimary and new test recipes, respectively, U and U′ are the numbers ofunder-killed defects for the primary and new test recipes, respectively,and γ is a proportionality constant relating the number of defects tothe number of bad panels, as shown by Equations (45), (47), (51), and(56).

[0195] Then, one can obtain, with the assumption O_(ATB)≅O′_(ATB),

I _(AR) −I′ _(AR)=(R+Q−U−O _(ATB))−(R+Q′−U′−O′_(ATB))≅(Q−Q′)−(U−U′),  (93)

[0196] where R is the number of bad panels with real defects.

[0197] From Equations (91), (92), and (93), one obtains:

I _(AR) −I′ _(AR) ≅ΔQ−ΔU=γ(ΔQ−ΔU).  (94)

[0198] Using Equation (94) in Equation (90), one obtains:

P≅γ(ΔQ−ΔU)C _(R)+(Y _(C)−(1−(1−Y _(C))U′/U))I _(C)(C _(M) +C_(MI))+((1−(1Y _(M))U′/U)(1−(1−Y _(C))U′/U)−Y _(M) Y _(C))P _(VALUE) I_(C).  (95)

[0199] VI. Profit Maximization by Threshold Optimization

[0200] The effect of a new thresholding test recipe on yields at thecell inspection stage 208 and the module inspection stage 212, and onthe productivity of the array repair equipment will now be described. Itwill also be shown how profit can be maximized by optimizingthresholding parameters.

[0201] As discussed above, in order to have a reference for optimizationof the thresholding parameters, the current test recipe of the arraytest equipment is called the primary test recipe, and its test result iscalled the primary test result. The current thresholding parameters ofVthi+, Vtlo+, Vthi−, and Vtlo− are called primary thresholdingparameters. If one wants to evaluate the effect of new thresholdingparameters on a production batch that has been already been processedthrough final module inspection using the primary test recipe, then onecan use the evaluation method that will now be described.

[0202] If the defective pixel voltage distribution is already known,then the number of under-killed defects for the primary test recipe canbe obtained by:

U=Unl+Unh+Upl+Uph,  (96)

[0203] where:

Unl=∫ _(Vtlo−) ^(Vde−) θnl dv, Unh=∫_(Vdb−) ^(Vthi−) θnh dv, Upl=∫_(Vtlo+) ^(Vdb+) θpl dv, Uph=∫ _(Vde+) ^(Vthi+) θph dv.

[0204] If the normal pixel voltage distribution is already known, thenthe number of over-killed defects for the primary test recipe can beobtained by:

Q=Qnl+Qnh+Qpl+Qph,  (97)

[0205] where:

Qnl=∫ _(−∞) ^(Vtlo−) Θn dv, Qnh=∫ _(Vthi−) ⁰ Θn dv, Qpl=∫ ₀ ^(Vtlo+) Θpdv, Qph=∫ _(Vthi+) ^(∞) Θp dv.

[0206] The Vtlo− thresholding value is scanned using variable vtlo−,while keeping the other threshold voltages at the fixed primary values.In this way, the number of under-killed and over-killed defects for thenew thresholding recipe can be obtained by:

U′=U′nl+Unh+Upl+Uph; and  (98)

Q′=Q′nl+Qnh+Qpl+Qph,  (99)

[0207] where:

U′nl=∫ _(vtlo−) ^(Vde−) θno dv and Q′nl=∫ _(−∞) ^(vtlo−) Θn dv.

[0208] From Equations (91), (92), and (96)-(99), one obtains:

ΔQ=Q−Q′=Qnl−Q′nl; and  (100)

ΔU=U−U′=Unl−U′nl.  (101)

[0209] From Equations (82), (83), (88), (89), (96), and (98), oneobtains:

Y′ _(C)=1−(1−Y _(C))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph);  (102)

E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph));  (103)

Y′ _(M)=1−(1−Y _(M))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph); and  (104)

E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y_(M))(1−(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph)).  (105)

[0210] From Equations (95), (96), (98), (100), and (101), one obtains:

P≅γ(Qnl−Q′nl−Unl+U′nl)C _(R)+(Y _(C)−(1−(1−Y_(C))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph)))I _(C)(C _(M) +C_(MI))+((1−(1−Y _(M))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph))(1−(1−Y_(C))(U′nl+Unh+Upl+Uph)/(Unl+Unh+Upl+Uph))−Y _(M) Y _(C))P _(VALUE) I_(C)  ((106)

[0211] Therefore, profit maximization can be achieved by taking themaximum value of P while the variable vtlo− is scanned around theprimary thresholding parameter of Vtlo−.

[0212] The Vthi− thresholding value can also be scanned using variablevthi−, while keeping the other thresholding voltages at the fixedprimary values. The number of under-killed and over-killed defects forthe new thresholding recipe can then be obtained by:

U′=Unl+U′nh+Upl+Uph; and  (107)

Q′=Qnl+Q′nh+Qpl+Qph,  (108)

[0213] where:

U′nh=∫ _(Vdb−) ^(vthi−) θnh dv and Q′nh=∫ _(vthi−) ^(θ) Θn dv.

[0214] From Equations (91), (92), (96), (97), (107), and (108), oneobtains:

ΔQ=Q−Q′=Qnh−Q′nh; and  (109)

ΔU=U−U′=Unh−U′nh.  (110)

[0215] From Equations (82), (83), (88), (89), (96), and (107), oneobtains:

Y′ _(C)=1−(1−Y _(C))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph);  (111)

E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph));  (112)

Y′ _(M)=1−(1−Y _(M))(Unl+U∝nh+Upl+Uph)/(Unl+Unh+Upl+Uph); and  (113)

E _(YM) ≡Y′ _(M) −Y _(M)−(1−Y_(M))(1−(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph)).  (114)

[0216] From Equations (95), (96), (107), (109), and (110), one obtains:

P≅γ(Qnh−Q∝nh−Unh+U′nh)C _(R)+(Y _(C)−(1−(1−Y_(C))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph)))I _(C)(C _(M) +C_(MI))+((1−(1−Y _(M))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph))(1−(1−Y_(C))(Unl+U′nh+Upl+Uph)/(Unl+Unh+Upl+Uph))−Y _(M) Y _(C))P _(VALUE) I_(C)  (115)

[0217] Therefore, profit maximization can be achieved by taking themaximum value of P, while the variable vthi− is scanned around theprimary parameter of Vthi−.

[0218] Thresholding value Vdo+ can also be scanned using variable vtlo+,while keeping the other thresholding voltages at the fixed primaryvalues. The number of under-killed and over-killed defects for the newthresholding recipe can then be obtained by:

U′=Unl+Unh+U′pl+Uph; and  (116)

Q′=Qnl+Qnh+Q′pl+Qph,  (117)

[0219] where:

U′pl=∫ _(vtlo+) ^(Vdb+) θpl dv and Q′pl=∫ _(θ) ^(vtlo+) Θp dv.

[0220] From Equations (91), (92), (96), (97), (116), and (117), oneobtains:

ΔQ=Q−Q′=Qpl−Q′pl; and  (118)

ΔU=U−U′=Upl−U′pl.  (119)

[0221] From Equations (82), (83), (88), (89), (96), and (116), oneobtains:

Y′ _(C)=1−(1−Y_(C))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph);  (120)

E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph));  (121)

Y′ _(M)=1−(1−Y _(M))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph); and  (122)

E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y_(M))(1−(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph))  (123)

[0222] From Equations (95), (96), (116), (118), and (119), one obtains:

P≅γ(Qpl−Q′pl−Upl+U′pl)C _(R)+(Y _(C)−(1−(1−Y_(C))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph)))I _(C)(C _(M) +C_(MI))+((1−(1−Y _(M))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph))(1−(1−Y _(C))(Unl+Unh+U′pl+Uph)/(Unl+Unh+Upl+Uph))−Y _(M) Y _(C))P _(VALUE) I_(C).  (124)

[0223] Therefore, profit maximization can be achieved by taking themaximum value of P, while the variable vtlo+ is scanned around theprimary parameter of Vtlo+.

[0224] Thresholding value Vthi+can also be scanned using variable vthi+,while keeping the other thresholding voltages at the fixed primaryvalues. The number of under-killed and over-killed defects for the newthresholding recipe can then be obtained by:

U′=Unl+Unh+Upl+U′ph; and  (125)

Q′=Qnl+Qnh+Qpl+Q′ph,  (126)

[0225] where:

U′ph=∫ _(Vde+) ^(cthi+) θph de and O′ph=∫ _(vthi+) ^(∞) Θp dv.

[0226] From Equations (91), (92), (96), (97), (125), and (126), oneobtains:

ΔQ=Q−Q′=Qph−Q′ph; and  (127)

ΔU=U−U′=Uph−U′ph.  (128)

[0227] From Equations (82), (83), (88), (89), (96), and (125), oneobtains:

Y′ _(C)=1−(1−Y _(C))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph);  (129)

E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph));  (130)

Y′ _(M)=1−(1−Y _(M))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph); and  (131)

E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y_(M))(1−(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph)).  (132)

[0228] From Equations (95), (96), (125), (127), and (128), one obtains:

P≅γ(Qph−Q′ph−Uph+U′ph)C _(R)+(Y _(C)−(1−(1−Y_(C))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph)))I _(C)(C _(M) +C_(MI))+((1−(1−Y _(M))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph))(1−(1−Y_(C))(Unl+Unh+Upl+U′ph)/(Unl+Unh+Upl+Uph))−Y _(M) Y _(C))P _(VALUE) I_(C).  (133)

[0229] Therefore, profit maximization can be achieved by taking themaximum value of P, while the variable vthi+ is scanned around theprimary parameter of Vthi+.

[0230] Thus, it has been shown how new values for the thresholdingparameters of Vtlo−, Vthi−, Vtlo+, and Vthi+ can be determined that givethe maximum profit when the defective and normal pixel voltagedistributions are already known. One can use the methodology describedabove to optimize the thresholding parameters based on presumed or knowndistributions of defective and normal pixel voltages.

[0231]FIG. 5 is a flow chart of a method of generating the distributionfunctions for normal pixels and defective pixels in an actual productionenvironment. All the equations having integral expressions should besolved in such a way that the integration is performed numerically bycounting the number of either good pixels for Θn and Θp, or the numberof defective pixels for θnl, θnh, θpl and θph, as the thresholdingparameter is scanned.

[0232] The method starts at step 500, and proceeds to step 505, where anew thresholding parameter set is used that will classify more pixels asdefects than those classified by the primary thresholding parameters.The resulting defect file is labeled “proto defect file”.

[0233] Then, at step 510, the proto defect file is reprocessed using theprimary thresholding parameters, in order to convert the proto defectfile to a primary defect file. The primary defect file is then comparedto the proto defect file, and the additional defective pixels reportedin the proto defect file are labeled “additional defects”.

[0234] Next, at step 515, the defective panels are repaired based oninformation in the primary defect file. The process proceeds to step520, where the cells are assembled and inspected.

[0235] Then, at step 525, the modules are assembled and inspected. Next,at step 530, if the “additional defects” are detected as real defectivepixels during the cell or module inspections, the “additional defects”are used to construct θnl, θnh, θpl, and θph in accordance with thepolarity and magnitude of the pixel voltages, as shown in FIG. 3. Theprocess then ends at step 535.

[0236] The analysis described above is applicable to a production linemodel that does not utilize the optional cell and module repair stages214 and 216. However, it should be appreciated that the analysisdescribed above can be adapted for a production line model that doesutilize the optional cell and model repair stages 214 and 216, whilestill falling within the scope of the present invention. Further, if theoptional cell and module repair stages 214 and 216 are used, but thecell and module repair rates are so low as to not make a significantcontribution to the yield rates, then the above-described analysis maybe applied.

[0237] VII. Profit Evaluation Using New Distribution Function TestRecipe

[0238] It was described above how profit can be maximized by optimizingthe thresholding parameters, based on the assumption that theunder-killed defects are the dominant cause of bad panels at the celland module inspection stages 208 and 212. In order to further improvethe profit, a new distribution function test recipe can also be appliedto the TFT-array test equipment.

[0239] In order to verify the effect of the new distribution functiontest recipe, one may split a very large production run into two groups,and test one group using the primary test recipe and the second groupusing the new distribution function test recipe. Then, the yields at thecell and module inspection stages 208 and 212 for each group can becompared. However, this method would take a long time due to the verylarge sample quantity required to minimize process fluctuations, andalso takes the high risk of sacrificing many sample units if one uses animproper new distribution function test recipe.

[0240] Thus, it is preferable to evaluate the new distribution functiontest recipe using the same production run that was already tested withthe primary test recipe, in order to obtain a fair comparison betweenthe primary and new distribution function test recipes, without the needfor large numbers of panels. The new distribution function test recipegenerates different distribution functions for normal and defectivepixel voltages from those generated by the primary test recipe, even forthe same sample production run. The effects of the new distributionfunction test recipe on the yield and profit are then evaluated.

[0241] First, at the array test stage 202, the sample production run istested with the primary test recipe, and the test results is labeled“primary defect file” (DF_(PRIME)). Then, the same sample production runis retested with the new distribution function test recipe, and thattest result is called “new defect file” (DF_(NEW)).

[0242] The sample production run then proceeds to the array repair stage204, and only the pixels commonly reported as defective in DF_(PRIME)and DF_(NEW) are reviewed by the operator of the TFT-array repairequipment. The operator then attempts to repair the pixels when thedefects are visually confirmed. The sample production run then proceedsto next stages, which is assumed to not include the optional cell andmodule repair stages 214 and 216.

[0243] For evaluation of the new distribution function test recipe, oneneeds to sort out the defects reported in DF_(PRIME) and DF_(NEW) basedon the repair actions performed on the defects, and the results of celland module inspections at the cell and module inspection stages 208 and212.

[0244] The table shown in FIG. 6 and the flow chart shown in FIG. 7illustrate how the results of the array test stage 202, array repairstage 204, cell inspection stage 208 and module inspection stage 212 areused to sort out the defective pixels discovered.

[0245] The process of FIG. 7 starts at step 700, and proceeds to steps705, where the DF_(PRIME) and DF_(NEW) are obtained from the table ofFIG. 6 and sorted as follows:

[0246] Common defects, CD=(GGc+GGm+OOn+GGcr+GGmr+GGr);

[0247] DF_(PRIME) unique defects, DPu=(GUc+GUm+OGn); and

[0248] DF_(NEW) unique defects, DNu=(UGc+UGm+GOn).

[0249] The process then continues to step 710 where, using the input tothe array repair stage 204, CD is sorted into:

[0250] CD1=(GGc+GGm+OOn); and

[0251] CD2=(GGcr+GGmr+GGr).

[0252] The array repair stage looks at only CD and parts of them aresorted as CD2 when a repair action is taken.

[0253] Next, at step 715, using the input to the cell inspection stage208, the following sorting is done:

[0254] CD1 into GGc and CD1a=(GGm+OOn);

[0255] CD2 into GGcr and CD2a=(GGmr+GGr);

[0256] DPu into GUc and DPu1=(GUm+OGn);

[0257] DNu into UGc and DNu1=(UGm+GOn); and

[0258] new cell defects as UUc.

[0259] Then, at step 720, using the input to the module inspectionstage, the following sorting is done:

[0260] CD1a into GGm and OOn;

[0261] CD2a into GGmr and GGr;

[0262] DPu1 into GUm and OGn;

[0263] DNu1 into UGm and GOn; and

[0264] new cell defect as UUm.

[0265] The process then ends at step 725. From FIG. 6, the total celldefect for the sample production (T_(CDc)) can be obtained as:

T _(CDc) =GGc+GUc+GGcr+UGc+UUc.  (134)

[0266] The effect of a new distribution function test recipe on the cellyield will now be considered. Total cell defect, if only the primarytest recipe had been applied, is shown in the table of FIG. 8, and isgiven by:

T _(CD) =T _(CDc) −Nc GUc,  (135)

[0267] because all GUc pixels should have been identified as defects andNc portion of them could have been repaired to good pixels and wouldhave increased GGr. GGr can be defined as:

GGr=GGrc+GGrm,  (136)

[0268] where GGrc is the number of good repaired pixels, which wouldhave been detected as defects at the cell inspection stage 208 had theynot been repaired, and GGrm is the number of good repaired pixels whichwould have been detected as defects at the module inspection stage 212had they nor been repaired. One can then assume that the number ofsuccessfully repaired pixels (Nc) would have followed the successfulrepair rate for the commonly detected defects, and obtain an expressionfor Nc as follows:

Nc=GGrc/(GGcr+GGrc).  (137)

[0269] One can assume that the successful repair rate of cell defects isthe same as that of module defects (GGcr:GGmr=GGrc:GGrm) and obtain:

GGrc=GGcr GGrm/GGmr.  (138)

[0270] From Equations (136) and (138), one obtains:

GGrc=GGcr(GGr−GGrc)/GGmr;  (139)

GGmr GGrc+GGcr GGrc=GGcr GGr; and  (140)

GGrc=GGcr GGr/(GGmr+GGcr).  (141)

[0271] From Equations (134), (135), (137) and (141), one obtains:

Nc=(GGcrGGr/(GGmr+GGcr))/(GGcr+(GGcrGGr/(GGmr+GGcr)))=GGcrGGr/(GGcr(GGmr+GGcr)+GGcrGGr)=GGr/(GGmr+GGcr+GGr); and  (142)

T _(CD) =T _(CDc) −Nc GUc=GGc+(1−Nc)GUc+GGcr+UGc+UUc.  (143)

[0272] From Equations (142) and (143), one obtains:

T _(CD) =GGc+(GGmr+GGcr)GUc/(GGrnr+GGcr+GGr)+GGcr+UGc+UUc.  (144)

[0273] Total cell defects, if only the new distribution function testrecipe had been applied, is shown in the table of FIG. 9, and is givenby:

T _(CD) =T _(CDc) −Nc UGc,  (145)

[0274] because all the UGc pixels should have been identified as defectsand Nc number of them could have been repaired to good pixels and wouldhave increased GGr.

[0275] From Equations (134) and (145), one obtains:

T _(CD) =T _(CDc) −Nc UGc=GGc+GUc+GGcr+(1−Nc)UGc+UUc.  (146)

[0276] From Equations (142) and (146), one obtains:

T′ _(CD) =GGc+GUc+GGcr+(GGmr+GGcr)UGc/(GGmr+GGcr+GGr)+UUc.  (147)

[0277] From Equations (143) and (146), the effect on total cell defects(ε_(TCD)) due to using the new distribution function test recipe onlyinstead of only the primary test recipe is given by:

ε_(TCD) =T′ _(CD) −T′ _(CD) =Nc UGc−Nc GUc=Nc(UGc−GUc).  (148)

[0278] From FIG. 6, the total module defects for the sample production(T_(MDc)) can be obtained as:

T _(MDc) =GGm+GUm+GGmr+UGm+UUm.  (149)

[0279] The effect of the new distribution function test recipe on themodule yield will now be considered. Total module defects, if only theprimary test recipe had been applied is shown in FIG. 8, and is givenby:

T _(MD) =T _(MDc) −Nm GUm,  (150)

[0280] because all GUm pixels should have been identified as defects,and Nm number of them could have been repaired to good pixels, whichwould have increased GGr. Then, one can assume that the portion ofsuccessfully repaired pixels follows the successful repair rate for thecommonly detected defects, and obtain the following expression for Nm:

Nm=GGrm/(GGmr+GGrm).  (151)

[0281] From Equation (138), one obtains:

GGrm=GGmr GGrc/GGcr.  (152)

[0282] From Equations (136) and (152), one obtains:

GGrm=GGmr(GGr−GGrm)/GGcr;  (153)

GGrm GGcr+GGmr GGrm=GGmr GGr; and  (154)

GGrm=GGmr GGr/(GGcr+GGmr).  (155)

[0283] From Equations (149), (150), (151) and (155), one obtains:

Nm=(GGmrGGr/(GGcr+GGmr))/(GGmr+(GGmrGGr/(GGcr+GGmr)))=GGmrGGr/(GGmr(GGcr+GGmr)+GGmrGGr)=GGr/(GGcr+GGmr+GGr); and  (156)

T _(MD) =T _(MDc) −NmGUm=GGm+(1−Nm)GUm+GGmr+UGm+UUm.  (157)

[0284] From Equations (156) and (157), one obtains:

T _(MD) =GGm+(GGcr+GGmr)GUm/(GGcr+GGmr+GGr)+GGmr+UGm+UUm.  (158)

[0285] Total module defects, if only the new distribution function testrecipe had been applied, is shown in FIG. 9, and is given by:

T′ _(MD) =T _(MDc) −Nm UGm,  (159)

[0286] because all UGm pixels should have been identified as defects,and Nm number of them could have been repaired to good pixels and wouldhave increased GGr.

[0287] From Equations (149) and (159), one obtains:

T′ _(MD) =T _(MDc) −NmUGm=GGm+GUm+GGmr+(1−Nm)UGm+UUm.  (160)

[0288] From Equations (156) and (160), one obtains:

T′ _(MD) =GGm+GUm+GGmr+(GGcr+GGmr)UGm/(GGcr+GGmr+GGr)+UUm.  (161)

[0289] From Equations (157) and (160), the effect on total moduledefects (ε_(TMD)) due to using the new distribution function test recipeonly instead of only the primary test recipe is given by:

ε_(TMD) =T _(MD) −T′ _(MD) =Nm UGm−Nm GUm=Nm(UGm−GUm).  (162)

[0290] The effect of the new distribution function test recipe onover-kill will now be considered. From Equation (91) and FIG. 6, one canobtain:

Number of over-killed panels of primary-test-only,Q=γQ=γ(OOn+OGn);  (163)

Number of over-killed panels of new-test-only, Q′=γQ′=γ(OOn+GOn);and  (164)

ΔQ=Q−Q′=γ(OGn−GOn).  (165)

[0291] In TFT-LCD manufacturing, because of the possibility ofunsuccessful repair work, the under-killed defects may not be the onlydominating source for bad panels at cell or module inspections. Thus,from Equations (45), (47), (51) and (56), one can assume that the rateof bad panels at the cell inspection stage 208 is proportional to thenumber of total cell defects, and obtain following expressions:

O _(CB) /I _(C) :T _(CD) =O′ _(CB) /I′ _(C) :T′ _(CD); and  (166)

O′ _(CB) /I′ _(C) =O _(CB) T′ _(CD)/(I _(C) T _(CD))).  (167)

[0292] From Equations (79) and (167), one obtains:

(I ^(C) −O′ _(CG))/I _(C)(I _(C) −O _(CG))T′ _(CD)/(I _(C) T _(CD));and  (168)

1−O′ _(CG) /I′ _(C)=(1−O _(CG) /I _(C))T′ _(CD))/T _(CD).  (169)

[0293] From Equations (11) and (169), one obtains:

Y′ _(C)=1−(1−Y _(C))T′ _(CD) /T _(CD).  (170)

[0294] Then, the improvement of cell inspection yield (E_(YC)) can beexpressed as:

E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y _(C))(1−T′ _(CD) /T _(CD)).  (171)

[0295] One can also assume that the rate of bad panels at the moduleinspection stage 212 is proportional to the number of total moduledefects, and obtain following expression:

O _(MB) /I _(M) :T _(MD) =O′ _(MB) /I′ _(M) :T′ _(MD).  (172)

[0296] Then, one obtains:

O′ _(MB) /I′ _(M) =O _(MB) T′ _(MD)/(I _(M) T _(MD)).  (173)

[0297] From Equation (173), since O_(MB)=I_(M)−O_(MG) without theoptional cell and module repair stages 214 and 216, one obtains:

(I′ _(M) −O′ _(MG))/I′ _(M)=(I _(M) −O _(MG))T′ _(MD)/(I _(M) T _(MD));and  (174)

1−O′ _(MG) /I′ _(M)=(1−O _(MG) /I _(M))T′ _(MD) /T _(MD).  (175)

[0298] From Equations (12) and (175), one obtains:

Y′ _(M)=1−(1−Y _(M))T′ _(MD) /T _(MD).  (176)

[0299] Then, the improvement in the module inspection yield (E_(YM)) canbe expressed as:

E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y _(M))(1−T′ _(MD) /T _(MD)).  (177)

[0300] Then, one can obtain an expression for the profit increase byusing Equations (170), (171), (176), (177), and (26), as follows:

P≅(I _(AR) −I′ _(AR))C _(R)+(Y _(C)−1)(1−T _(CD) /T _(CD))I _(C)(C _(M)+C _(MI))+((1−(1−Y _(M))T′ _(MD) /T _(MD))(1−(1−Y _(C))T′_(CD) /T_(CD))−Y _(M) Y _(C))P _(VALUE) I _(C).  (178)

[0301] Using Equation (94) in Equation (178), one obtains:

P≅(ΔQ−ΔU)C _(R)+(Y _(C)−1)(1−T _(CD) /T _(CD))I _(C)(C _(M) +C_(MI))+((1−(1−Y _(M))T′ _(MD) /T _(MD))(1−(1−Y _(C))T′_(CD) /T _(CD))−Y_(M) Y _(C))P _(VALUE) I _(C).  (179)

[0302] The effect of the new distribution function test recipe onunder-kill will now be considered. From Equation (92) and FIG. 6, onecan obtain:

Number of under-killed panels of primary-test-only,U=γU=γ(UGc+UUc+UGm+UUm); and  (180)

Number of under-killed panels of new-test-only,U′=γU′=γ(GUc+GUm+UUc+UUm),  (181)

[0303] where U and U′ are the numbers of under-killed defects for theprimary and new distribution function test recipes, respectively. FromEquations (92), (180) and (181), one obtains the following expressionfor the effect of the new distribution function test recipe on theunder-killed panels:

ΔU=U−U′=γ(UGc+UGm−GUc−GUm).  (182)

[0304] Using Equations (165) and (182) in Equation (179), one obtains:

P≅γ(OGn−GOn−UGC−UGm+GUC+GUm)C _(R)+(Y _(C)−1)(1−T′ _(CD) /T _(CD))I_(C)(C _(M) +C _(MI))+((1−(1−Y _(M))T′ _(MD) /T _(MD))(1−(1−Y)T′ _(CD)/T _(CD))−Y _(M) Y _(C))P _(VALUE) I _(C).  (183)

[0305] The values of Y_(C) and Y_(M) can be obtained from a recentproduction that was tested with the primary test recipe, under theassumption that the yields between the recent and sample productions arethe same. The values of Y_(C) and Y_(M) can also be obtained from thesample production, as will now be explained.

[0306] One can obtain expressions for Y_(C) and Y_(M), similar to theexpressions for Y′_(C) and Y′_(M) shown in Equations (170) and (176),from the assumption that the rate of bad panels at cell and moduleinspection stages 208 and 212 is proportional to the number of totalcell and module defects:

Y _(C)=1−(1−Y _(Cc))T _(CD) /T _(CDc); and  (184)

Y _(M)=1−(1−Y _(Mc))T _(MD) /T _(MDc),  (185)

[0307] where Y_(Cc) and Y_(Mc) are the cell and module yields,respectively, for the sample production in which only the pixelscommonly reported as defects in DF_(PRIME) and DF_(NEW) are sent to theTFT-array repair equipment.

[0308] From Equations (134), (144), (149), (158), (184) and (185), oneobtains:

Y _(C)=1−(1−Y_(Cc))(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)/(GGc+GUc+GGcr+UGc+UUc);and  (186)

Y _(M)=1−(1−Y_(MC))(GGm+(GGcr+GGmr)GUm/(GGcr+GGmr+GGr)+GGmr+UGm+UUm)/(GGm+GUm+GGmr+UGm+UUm).  (187)

[0309] The values of I_(C), I′_(AR), and I_(M) can be obtained from therecent production with the same quantity of I_(A) that was tested withthe primary test recipe, under the assumption that the yields are thesame between the recent and sample productions. The values of I_(C),I_(AR), and I_(M) can also be obtained from the sample production, aswill now be described.

[0310] In regular production of TFT-LCDs, one can assume thatO_(ATB)+O_(ARB)≅O_(ATBc)+O_(ARBc) (c denotes the sample production),because the bad panels usually go to next process stage as a portion ofthe larger TFT-array base plate. If the assumption

O _(ATB) +O _(ARB) ≅O _(ATBc) +O _(ARBc)  (188)

[0311] is valid, then with

I _(C) =I _(A)−(O _(ATB) +O _(ARB)) and  (189)

I _(Cc) =I _(A)−(O _(ATBc) +O _(ARBc)),  (190)

[0312] one obtains:

I _(C) ≅I _(Cc)  (191)

[0313] From Equations (93), (163), (164), (180), (181) and FIG. 6, oneobtains the following expressions for the sample production, in whichonly the defects detected both by the primary and new distributionfunction test recipes are sent to the TFT-array repair equipment:

I _(AR) −I _(ARc)=(R+Q−U−O _(ATB))−(R+Qc−Uc−O_(ATBc))≅(Q−Qc)−(U−Uc),  (192)

[0314] where O_(ATB)−O_(ATBc)≅0 is assumed;

Over-killed panels of sample production, Qc=Q∩Q′=γOOn; and  (193)

Under-killed panels of sample production,Uc=U∪U′=γ(UGc+UUc+UGm+UUm+GUc+GUm).  (194)

[0315] From Equations (163), (180), (192), (193) and (194), one obtains:

I _(AR) −I_(ARc)≅γ(OOn+OGn−OOn)−γ(UGc+UUc+UGm+UUm−(UGc+UUc+UGm+UUm+GUc+GUm))=γ(OGn+GUc+GUm).  (195)

[0316] The value of γ can be obtained with the assumption that O_(ATBc)is very small compared with other parameters. From Equations (192),(193), (194) and FIG. 6, one obtains:

I _(ARc)=R+Qc−Uc=γ(GGc+GUc+GGm+GUm+GGcr+GGmr+GGr+UGc+UUc+UGm+UUm+OOn−(UGc+UUc+UGm+UUm+GUc+GUm))=γ(GGc+GGm+GGcr+GGmr+GGr+OOn).  (196)

[0317] Thus, from Eq. (196), one obtains:

γ=I _(ARc)/(GGc+GGm+GGcr+GGmr+GGr+OOn)  (197)

[0318] From Equations (195) and (197), one obtains:

I _(AR)≅γ(OGn+GUc+GUm)+I _(ARc) =I_(ARc)(OGn+GUc+GUm)/(GGc+GGm+GGcr+GGmr+GGr+OOn)+I _(ARc) −I_(ARc)(OGn+GUc+GUm+GGc+GGm+GGcr+GGmr+GGr+OOn)/(GGc+GGm+GGcr+GGmr+GGr+OOn).  (198)

[0319] From FIG. 2, without the optional cell and module repair stages214 and 216, and Equation (191), one obtains:

I _(M=O) _(CG) =I _(C) −O _(CB); and  (199)

I _(Mc) =O _(CGc) =I _(Cc) −O _(CBc) −I _(C) −O _(CBc).  (200)

[0320] From Equations (199) and (200), one obtains:

I _(M) ≅I _(Mc) +O _(CBc) −O _(CB).  (201)

[0321] From Equation (45), (47), (51) and (56), one can assume that thenumber of bad panels at the cell inspection stage 208 is proportional tothe number of total cell defects, and obtain the following expressions:

O _(CB) =δT _(CD); and  (202)

O _(CBc) =δT _(CDc),  (203)

[0322] where δ is a proportionality constant.

[0323] From Equations (134) and (203), one obtains:

δ=O _(CBc) /T _(CDc) =O _(CBc)/(GGc+GUc+GGcr+UGc+UUc).  (204)

[0324] From Equations (144), (202) and (204), one obtains:

O _(CB)=(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)

[0325] O_(CBc)/(GGc+GUc+GGcr+UGc+UUc).  (205)

[0326] Thus, from Equations (201) and (205), one obtains:

I _(M) ≅I _(Mc) +O _(CBc)−(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+

[0327] UGc+UUc)O _(CBc)/(GGc+GUc+GGcr+UGc+UUc)=I _(Mc) +O_(CBc)(1−(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)/(GGc+GUc+GGcr+UGc+UUc)).  (206)

[0328] Using Equations (134), (144), (147), (149), (158), (161), (184),(185), (186), (187), (191) and (197) in Equation (183), one obtains:

P≅(I _(ARc)/(GGc+GGm+GGcr+GGmr+GGr+OOn))(OGn−GOn−UGc−UGm+GUc+GUm))C_(R)+((Y_(Cc)−1)(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)/(GGc+GUc+GGcr+UGc+UUc))(1−(GGc+GUc+GGcr+(GGmr+GGcr)UGc/(GGmr+GGcr+GGr)+UUc)/(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc))I_(Cc)(C _(M) +C _(MI))+((1−(1−Y_(Mc))(GGm+GUm+GGmr+(GGcr+GGmr)UGm/(GGcr+GGmr+GGr)+UUm)/(GGm+GUm+GGmr+UGm+UUm))(1−(1−Y_(Cc))(GGc+GUc+GGcr+(GGmr+GGcr)UGc/(GGmr+GGcr+GGr)+UUc)/(GGc+GUc+GGcr+UGc+UUc))−(1−(1−Y_(MC))(GGm+(GGcr+GGmr)GUm/(GGcr+GGmr+GGr)+GGmr+UGm+UUm)/(GGm+GUm+GGmr+UGm+UUm))(1−(1−Y_(Cc))(GGc+(GGmr+GGcr)GUc/(GGmr+GGcr+GGr)+GGcr+UGc+UUc)/(GGc+GUc+GGcr+UGc+UUc)))P_(VALUE) I _(Cc).  (207)

[0329] The analysis described above is applicable to a production linemodel that does not utilize the optional cell and module repair stages214 and 216. However, it should be appreciated that the analysisdescribed above can be adapted for a production line model that doesutilize the optional cell and model repair stages 214 and 216, whilestill falling within the scope of the present invention. Further, if theoptional cell and module repair stages 214 and 216 are used, but thecell and module repair rates are so low as to not make a significantcontribution to the yield rates, then the above-described analysis maybe applied.

[0330] VIII. Threshold Optimization with No Assumption about Defects

[0331] The threshold optimization methodology described above is basedon the assumption that the under-killed defects are the only dominantcause of bad panels at cell and module inspections. Thresholdoptimization can also be done without the assumption that theunder-killed defects are the only dominant cause of the bad panels atcell and module inspections.

[0332]FIG. 10 is a flow chart showing how profit maximization for theTFT-LCD production line can be achieved by optimization of thethresholding parameters. The process begins at step 1000, and proceedsto step 1005, where the TFT-array panels are tested, at the array teststage 202, by TFT-array test equipment. The testing is done with “protothresholding” parameters, which are tighter than the primarythresholding parameters of the primary test recipe. The generated protodefects (PD) file identifies more defective pixels than the normalproduction defects file generated by the primary thresholding. At step1005, the primary thresholding parameters are set as “screenthresholding parameters” (Pth).

[0333] Next, at step 1010, initial defect sorting is performed for thePD file, in accordance with the flow chart of FIG. 11, in which primarythresholding parameters are applied to the proto defects file as screenthresholding parameters (Pth) to screen the PD file and generate ascreened defects (SD) file that is identical to the normal defects filegenerated by the primary thresholding.

[0334] Referring to FIG. 11, the initial defect sorting process startsat step 1100, and proceeds to step 1105, where the screened defects (SD)file is generated by using screen thresholding, which screens the PDfile by less stringent thresholding parameters than proto thresholdingparameters. Then, at step 1110, the SD is reviewed and the panels thatare visually confirmed as defective are repaired. The SD that has beenrepaired is noted as SDrp and is divided into two groups as follows: (1)Successfully repaired pixel (noted as Well)—no defect observed at laterinspections; and (2) Still defective due to improper repair: The defectis observed at either cell inspection (noted as CSDrp) or moduleinspection (noted as MSDrp).

[0335] An SD that has not been repaired is noted as SDnr and is dividedinto two groups as follows: (1) Over-kill at array test (noted as Q)—nodefect observed at later inspections; and (2) Defect due to impropervisual judge—Defect observed at either cell inspection (noted as CSDnr)or module inspection (noted as MSDnr).

[0336] Next, at step 1115, cell inspection confirms the defects reportedbefore and changes the notation as follows:

PD→CPD SDrp→CSDrp SDnr→CSDnr.

[0337] In addition, cell inspection detects new defects (noted as CND):ND→CND.

[0338] Then, at step 1120, module inspection confirms the defectsreported before and changes the notation as follows:

PD→MPD SDrp→MSDrp SDnr→MSDnr.

[0339] Also, module inspection detects new defects (noted as MND):ND→MND.

[0340] If the cell defects are repaired after the cell inspection, thenadditional sorting is done as follows:

[0341] (1) Module inspection confirms the defects reported by cellinspection and changes the notation as follows:

CPD→MCPD CSDrp→MCSDrp CSDnr→MCSDnr CNDΘMCND; and

[0342] (2) Module inspection confirms the success of repair action doneafter cell inspection, and changes the notation as follows:

CPD→RMCPD CSDrp→RMCSDrp CSDnr→RMCSDnr CND→RMCND

[0343] The process then ends at step 1125.

[0344] Referring back to FIG. 10, the result of the initial defectsorting shown in FIG. 11 is calculated at step 1015 as follows:

Cell defect(T _(CD))=CPD+CSDrp+CSDnr+CND;  (208)

Module defect(T _(MD))=MPD+MSDrp+MSDnr+MND; and  (209)

Over-kill(Q)=SDnr−(CSDnr+MSDnr).  (210)

[0345] After initial defect sorting, the screen thresholding parametersare scanned through the primary thresholding parameters in each zone, sothat they can be either tighter or looser than the primary thresholdingparameters, but not tighter than the proto thresholding parameters.

[0346] Whenever any of the screen thresholding parameters changes itsvalue, defect resorting is done (step 1020) by applying the newparameter to the PD file to determine the effects of the changedparameter. Next, at step 1025, the benefit of the defect resorting iscalculated. The process then proceeds to step 1030, where a decision ismade as to whether to continue scanning Pth, whose span is set by theuser around primary thresholding parameters with a restriction that Pthdoes not become tighter than the proto thresholding. If it is decided tocontinue scanning Pth, the process jumps to step 1050. Otherwise, theprocess continues to step 1035.

[0347] At step 1035, the optimum screen thresholding parameters (Pth) ischosen among all the screen thresholding parameters evaluated and itsbenefit is determined. Next, at step 1040, a decision is made as towhether to try additional screen thresholding parameters based on thebenefit determined at step 1035. If it is decided to try additionalscreen thresholding parameters, the process proceeds to step 1050.Otherwise, the process ends at step 1045.

[0348] At step 1050, the screen thresholding parameters are updated, andthe process jumps back to step 1020.

[0349]FIG. 12 is a flow chart showing the method used for defectresorting (step 1020 of FIG. 10). The process starts at step 1200, andproceeds to step 1205, where it is determined if the screen thresholdingis equal to, tighter than, or looser than the primary thresholding. Ifthe screen thresholding is looser than the primary thresholding, thenthe process jumps to step 1220. If the screen thresholding is equal tothe primary thresholding, then the process jumps to step 1230, where theprocess ends.

[0350] If the screen thresholding is tighter than the primarythresholding, then the process proceeds to step 1210, where a newscreened defects (SD′) file is generated by using tighter screenthresholding. Tighter screen thresholding decreases the number of PD,increases the number of SD, and decreases the number of CPD and MPDcompared to those of primary thresholding. The portion of decrease inthe total cell or module defects is given by Rwell, which is defined asthe number of well repaired pixel divided by the number of real defectsthat the repair operator reviews and is expressed as(SDrp−CSDrp−MSDrp)/(SD−Q), based on the assumption that the repair rateis maintained as constant.

[0351] At step 1215, the change in CPD (ΔCPD), the change in MPD (ΔMPD)and the change in SD (ΔSD) are calculated. The amount of increase ofover-killed defects is given by subtracting the increase of real defectdetection, (ΔCPD+ΔMPD), from the increase of screened defects, ΔSD.Thus, when the scanned thresholding parameters are tighter than theprimary thresholding parameters, the cell and module defects andover-kill defects are as follows:

T′ _(CD) =CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−Q);  (211)

T′ _(MD) =MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−Q); and  (212)

Q′=SDnr−(CSDnr+MSDnr)+ΔSD−(ΔCPD+ΔMPD). (213)

[0352] Other parameters can be obtained in a similar way as follows:

Cell under-kill, CPD′=CPD−ΔCPD;  (214)

CSD′rp=CSDrp+(ΔCPD+ΔMPD)CSDrp/(SD−Q);  (215)

CSD′nr=CSDnr+(ΔCPD+ΔMPD)CSDnr/(SD−Q);  (216)

Module under-kill, MPD′=MPD−ΔMPD;  (217)

MSD′rp=MSDrp+(ΔCPD+ΔMPD)MSDrp/(SD−Q);  (218)

MSD′nr=MSDnr+(ΔCPD+ΔMPD)MSDnr/(SD−Q);  (219)

MCPD′=MCPD−ΔCPD;  (220)

MCSD′rp=MCSDrp+(ΔCPD+ΔMPD)MCSDrp/(SD−Q); and  (221)

MCSD′nr=MCSDnr+(ΔCPD+ΔMPD)MCSDnr/(SD−Q).  (222)

[0353] From Equations (208) and (211), the change in total cell defects(ε_(TCD)) due to tighter thresholding parameters is given by:

ε_(TCD) =T _(CD) −T′ _(CD) =ΔCPD(SDrp−CSDrp−MSDrp)/(SD−Q).  (223)

[0354] From Equations (209) and (212), the change in total moduledefects (ε_(TMD)) due to tighter thresholding parameters is given by:

ε_(TMD) =T _(MD) −T′ _(MD) =ΔMPD(SDrp−CSDrp−MSDrp)/(SD−Q).  (224)

[0355] From Equations (210) and (213), the change in over-kill defects(ΔQ) due to tighter thresholding parameters is given by:

ΔQ=Q−Q′=ΔCPD+ΔMPD−ΔSD.  (225)

[0356] From Equations (214) and (217), the change in under-kill defects(AU) due to tighter thresholding parameters is given by:

ΔU=U−U′=(CPD+MPD)−(CPD′+MPD′)=(CPD+MPD)−(CPD−ΔCPD+MPD−ΔMPD)=ΔCPD+ΔMPD.  (226)

[0357] From Equations (170), (171), (176), (177), (208), (209), (211),and (212), one obtains:

Y′ _(C)=1−(1−Y_(C))(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(CPD+CSDrp+CSDnr+CND);  (227)

E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y_(C))(1−(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(CPD+CSDrp+CSDnr+CND));  (228)

Y′ _(M)=1−(1−Y_(M))(MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(MPD+MSDrp+MSDnr+MND);and  (229)

E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y _(M))(1−(MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−

[0358] CSDrp−MSDrp)/(SD−Q))/(MPD+MSDrp+MSDnr+MND)).  (230)

[0359] From Equations (94), (179), (208), (209), (211), (212), (225),and (226), one can obtain the expression for the profit increase fromusing the tighter thresholding parameters:

P≅γΔSD C _(R)+(Y_(C)−1)(1−(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(CPD+CSDrp+CSDnr+CND))I_(C)(C _(M) +C _(MI))+((1−(1−Y_(M))(MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(MPD+MSDrp+MSDnr+MND))(1−(1−Y_(C))(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(CPD+CSDrp+CSDnr+CND))−Y_(M) Y _(C))P _(VALUE) I _(C).  (231)

[0360] The value of γ can be obtained with the assumption that O_(ATB)is very small compared with other parameters, as will now be described.From Equations (91), (92), (93), (210) and (226), one obtains:

I _(AR)=γ(R+Q−U)−O_(ATB)≅γ(R+Q−U)=γ((CPD+MPD+SD−Q)+Q−(CPD+MPD))=γSD,  (232)

[0361] where R is the number of real defects before repair, and is givenby:

R=CPD+MPD+SD−Q.  (233)

[0362] Thus, from Equation (232), one obtains:

γ=I _(AR) /SD.  (234)

[0363] From Equations (231) and (234), one obtains:

P≅−ΔSD C _(R) I _(AR) /SD+(Y_(C)−1)(1−(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(CPD+CSDrp+CSDnr+CND))I_(C)(C _(M) +C _(MI))+((1−(1−Y_(M))(MPD+MSDrp+MSDnr+MND−ΔMPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(MPD+MSDrp+MSDnr+MND))(1−(1−Y_(C))(CPD+CSDrp+CSDnr+CND−ΔCPD(SDrp−CSDrp−MSDrp)/(SD−Q))/(CPD+CSDrp+CSDnr+CND))−Y_(M) Y _(C))P _(VALUE) I _(C).  (235)

[0364] The values of Y_(C), Y_(M), I_(AR), and I_(C) can be obtainedfrom the sample production runs using the primary thresholdingparameters.

[0365] The use of looser screen thresholding parameters decreases thenumber of SD and successfully repaired pixels, increases the number ofPD, and increases the number of CPD and MPD, compared to using theprimary thresholding parameters. In order to analyze the effects oflooser screen thresholding parameters, the results of the primarythresholding parameters, given by Equations (208) and (209), areexpressed in a different format as follows:

T _(CD) =CPD+CSDrp+CSDnr+CND=CPD+CSD′rp+CSD′nr+ΔCSDrp+ΔCSDnr+CND;and  (236)

T _(MD) =MPD+MSDrp+MSDnr+MND=MPD+MSD′rp+MSD′nr+ΔMSDrp+ΔMSDnr+MND,  (237)

[0366] where ΔCSDrp indicates the number of CSDrp that are converted toCPD and is obtained by (CSDrp−CSD′rp), ΔCSDnr indicates the number ofCSDnr that are converted to CPD and is obtained by (CSDnr−CSD′nr),ΔMSDrp indicates the number of MSDrp that are converted to MPD and isobtained by (MSDrp−MSD′rp), and ΔMSDnr indicates the number of MSDnrthat are converted to MPD and is obtained by (MSDnr−MSD′nr).

[0367] The increase in the cell or module defects, which is due to thereduction of the number of successfully repaired pixels, is given by Rwcand Rwm, respectively, based on the assumption that the reverse rate ofunder-kill defects from the successfully repaired pixels remainsconstant, and is determined by the following ratios of under-killdefects for the primary thresholding parameters:

Rwc=Number of cell under-kill defects/Total number of under-killdefects=CPD/(CPD+MPD); and  (238)

Rwm=Number of module under-kill defects/Total number of under-killdefects=MPD/(CPD+MPD).  (239)

[0368] Thus, when the scanned thresholding parameters are looser thanthe primary thresholding parameters, the cell and module defects aregiven as follows (from Equations (208), (209), (238), and (239)):

T′ _(CD) =T _(CD) +ΔWell Rwc=CPD+CSDrp+CSDnr+CND+ΔWell CPD/(CPD+MPD);and  (240)

T′ _(MD) =T _(MD) +ΔWell Rwm=MPD+MSDrp+MSDnr+MND+ΔWellMPD/(CPD+MPD),  (241)

[0369] where ΔWell is the portion of successfully repaired pixels withprimary thresholding that would not have been detected with looserthresholding, and become either cell or module under-kill defects. Withlooser thresholding, the number of over-killed defects is decreasedbecause some portion of Q (ΔQ) would not have been reported as defects.From FIG. 11, one obtains:

SD=SDrp+SDnr; and  (242)

SDrp=CSDrp+MSDrp+Well,  (243)

[0370] where Well is the number of successfully repaired defects. FromEquations (210), (242) and (243), one obtains the following expressionfor ΔQ:

ΔQ=Q−Q′=(SDnr−(CSDnr+MSDnr))−(SD′nr−(CSD′nr+MSD′nr))=(SD−SDrp−(CSDnr+MSDnr))−(SD′−SD′rp−(CSD′nr+MSD′nr))=(SD−(CSDrp+MSDrp+Well)−(CSDnr+MSDnr))−(SD′−(CSD′rp+MSD′rp+W′ell)−(CSD′nr+MSD′nr))=(SD−SD′)−(CSDrp−CSD′rp+MSDrp−MSD′rp+Well−W′ell)−(CSDnr−CSD′nr+MSDnr−MSD′nr)=ΔSD−ΔCSDrp−ΔCSDnr−ΔMSDrp−ΔMSDnr−Δwell.  (244)

[0371] Other parameters can be obtained by similar way as follows:

Cell under-kill, CPD′=CPD+ΔCSDrp+ΔCSDnr+ΔWell Rwc;  (245)

CSD′rp=CSDrp−ΔCSDrp;  (246)

CSD′nr=CSDnr−ΔCSDnr;  (247)

Module under-kill, MPD′=MPD+ΔMSDrp+ΔMSDnr+ΔWell Rwm;  (248)

MSD′rp=MSDrp−ΔMSDrp;  (249)

MSD′nr=MSDnr−ΔMSDnr;  (250)

MCPD′=MCPD+ΔCSDrp+ΔCSDnr+ΔWell Rwc;  (251)

MCSD′rp=MCSDrp−ΔMCSDrp; and  (252)

MCSD′nr=MCSDnr−ΔMCSDnr.  (253)

[0372] From Equations (236) and (240), the effect of looser thresholdingparameters over the primary thresholding parameters on the total celldefects (ε_(TCD)) is obtained by:

ε_(TCD) =T _(CD) −T′ _(CD))=−ΔWell Rwc=−ΔWell CPD/(CPD+MPD).  (254)

[0373] From Equations (237) and (241), the effect of looser thresholdingparameters over the primary thresholding parameters for the total moduledefects (ε_(TMD)) is obtained by

ε_(TMD) =T _(MD) −T′ _(MD) =−ΔWell Rwm=−ΔWell MPD/(CPD+MPD).  (255)

[0374] From Equations (238), (239), (245) and (248), the effect oflooser thresholding parameters over the primary thresholding parametersfor the under-kill defects (ΔU) is obtained by:

ΔU=U−U′=(CPD+MPD)−(CPD′+MPD′)=(CPD+MPD)−(CPD+ΔCSDrp+ΔCSDnr+ΔWellRwc+MPD+ΔMSDrp+ΔMSDnr+ΔWell Rwm)=−(ΔCSDrp+ΔCSDnr+ΔWellRwc+ΔMSDrp+ΔMSDnr+ΔWellRwm)=−(ΔCSDrp+ΔCSDnr+ΔWell+ΔMSDrp+ΔMSDnr).  (256)

[0375] From Equations (170), (171), (176), (177), (236), (237), (240)and (241), one obtains:

Y′ _(C)=1−(1−Y _(C))(CPD+CSDrp+CSDnr+CND+ΔWellCPD/(CPD+MPD))/(CPD+CSDrp+CSDnr+CND);  (257)

E _(YC) ≡Y′ _(C) −Y _(C)=(1−Y _(C))(1−(CPD+CSDrp+CSDnr+CND+ΔWellCPD/(CPD+MPD))/(CPD+CSDrp+CSDnr+CND));  (258)

Y′ _(M)=1−(1−Y _(M))(MPD+MSDrp+MSDnr+MND+ΔWellMPD/(CPD+MPD))/(MPD+MSDrp+MSDnr+MND); and  (259)

E _(YM) ≡Y′ _(M) −Y _(M)=(1−Y _(M))(1−(MPD+MSDrp+MSDnr+MND+ΔWellMPD/(CPD+MPD))/(MPD+MSDrp+MSDnr+MND)).  (260)

[0376] From Equations (244) and (256), one obtains:

ΔQ−ΔU=ΔSD.  (261)

[0377] From Equations (94), (179), (234), (236), (237), (240), (241) and(261), one can obtain the expression for the profit increase resultingfrom the looser thresholding parameters as follows:

P≅ΔSD C _(R) I _(AR) /SD+(Y _(C)−1)(1−(CPD+CSDrp+CSDnr+CND+ΔWellCPD/(CPD+MPD))/(CPD+CSDrp+CSDnr+CND))I _(C)(C _(M) +C _(MI))+((1−(1−Y_(M))(MPD+MSDrp+MSDnr+MND+ΔWellMPD/(CPD+MPD))/(MPD+MSDrp+MSDnr+MND))(1−(1−Y_(C))(CPD+CSDrp+CSDnr+CND+ΔWell CPD/(CPD+MPD))/(CPD+CSDrp+CSDnr+CND))−Y_(M) Y _(C))P _(VALUE) I _(C).  (262)

[0378] If the cell defects are repaired after the cell inspection stage208, then the successful rate of cell repair, Rcell, can be obtainedfrom FIG. 11 as follows:

Rcell=(RMCPD+RMCSDrp+RMCSDnr+RMCND)/(CPD+CSDrp+CSDnr+CND).  (263)

[0379] Once the profit maximization has been achieved for one screenthresholding parameter, then another profit maximization process isperformed for another screen thresholding parameter in its scanningzone. This profit maximization process is repeated for all remainingscreen thresholding parameters. The data for profit maximization shouldbe obtained from the entire sample production runs, and the optimumscreen thresholding parameters are preferably chosen that will maximizethe profit for the entire production run.

[0380] The analysis described above is applicable to a production linemodel that does not utilize the optional cell and module repair stages214 and 216. However, it should be appreciated that the analysisdescribed above can be adapted for a production line model that doesutilize the optional cell and model repair stages 214 and 216, whilestill falling within the scope of the present invention. Further, if theoptional cell and module repair stages 214 and 216 are used, but thecell and module repair rates are so low as to not make a significantcontribution to the yield rates, then the above-described analysis maybe applied.

[0381] IX. Profit Maximization of Both Primary and New Test

[0382] Profit maximization for both new and primary test recipes usingthe same sample production runs will now be described. FIGS. 13A-13Dillustrate a flow chart for profit maximization of new and primary testrecipes.

[0383] The process starts at step 1300, and proceeds to step 1302, wheresample production runs are tested by the TFT-array test equipment at thearray test stage (AT) with a primary distribution function test recipeand primary thresholding parameters (θ_(PRIME)). The test result islabeled primary defect files (DF_(PRIME)). Then, the same sampleproduction runs are retested with the primary distribution function testrecipe and 1^(st) proto thresholding, and the test result is labeled“1^(st) PD file.” Then, the same sample production runs are retestedwith a new distribution function test recipe and 2^(nd) protothresholding, and the test result is called “2^(nd) PD file.”

[0384] Then, at step 1304, thresholding for the new distributionfunction test recipe (θ_(NEW)), which is looser than the 2^(nd) protothresholding, is applied to the 2^(nd) PD file to generate defect fileslabeled DF_(NEW). Next, at step 1306, the sample production runs proceedto the TFT-array repair stage 204 and, as described above in SectionVII, only the pixels commonly reported as defects in DF_(PRIME) andDF_(NEW) are reviewed by the operator of the TFT-array repair equipment,and the operator attempts to repair the pixels when the defects arevisually confirmed. The sample production runs then proceed to nextprocess stage, which is assumed to have not include the optional celland module repair stages 214 and 216.

[0385] For evaluation of new distribution function test recipe, asdescribed above in Section VII, the defects reported in DF_(PRIME) andDF_(NEW) are sorted out based on the repair actions performed on thedefects and the results of cell and module inspections. Then, at step1308, the effect of the new distribution function test recipe iscalculated, as described above in Section VII.

[0386] At step 1310, it is decided whether to continue tuning θ_(NEW),whose span is set by the user around the starting θ_(NEW) in step 1304with a restriction that θ_(NEW) does not become tighter than the 2^(nd)proto thresholding. If the decision is made to not continue θ_(NEW)scanning, then the process jumps to step 1326 (FIG. 13C). Otherwise, theprocess continues to step 1312.

[0387] At step 1312, θ_(NEW) is updated and applied to the 2^(nd) PDfile to generate an SD′_(NEW) file. Next, at step 1314, it is determinedif θ_(NEW) has been updated to tighter or looser thresholding. Ifθ_(NEW) is updated to tighter thresholding, then the process proceeds tostep 1318, where the values of GUc, GUm, OGn, UUc, UUm and GGn decreaseby ΔGUc, ΔGUm, ΔOGn, ΔUUc, ΔUUm, and ΔGGn, respectively, because theSD′_(NEW) files report these as additional defects. FIG. 14 is a tableshowing how the defect sorting result is modified by the additionaldefects. In the table of FIG. 14, GGcr is increased by (1−Nc) ΔGUc, GGmrby (1−Nm) ΔGUm, and GGr by Nc ΔGUc+Nm ΔGUm, based on the sameassumptions used in the table of FIG. 8 above.

[0388] If θ_(NEW) is updated to looser thresholding, the processproceeds to step 1316, where the values of GGc, GGm, OOn, GGcr, GGmr,GGr, UGc, UGm, and GOn decrease by ΔGGc, ΔGGm, ΔOOn, ΔGGcr, ΔGGmr, ΔGGr,ΔUGc, ΔUGm, and ΔGOn, respectively, because these are included in the2^(nd) PD files, but not included in the SD′_(NEW) files as defects.FIG. 15 is a table showing how the defect sorting result is modified bythe decrement of reported defects in the SD′_(NEW). In the table of FIG.15, GUc is increased by ΔGGc+ΔGGcr+ΔGGr GUc/(GUc+GUm) and GUm isincreased by ΔGGm+ΔGGmr+ΔGGr GUm/(GUc+GUm), based on the assumption thatthe reverse rate to GUc or GUm from the successfully repaired pixelswhen θ_(NEW) becomes looser is maintained constant and is determined bythe ratio of GUc and GUm for the starting θ_(NEW).

[0389] Once the parameters are updated, as shown in the tables of FIG.14 or 15, then the effect of the new θ_(NEW) can be obtained by usingthe analysis of Section VII. Therefore, profit maximization can beachieved by taking the maximum value of P while θ_(NEW) is scannedthrough the starting θ_(NEW) in its scanning zone. Once the profitmaximization has been achieved for one θ_(NEW) parameter, then anotherprofit maximization process is performed for another θ_(NEW) parameterin its scanning zone. This profit maximization process is repeated forall the remaining θ_(NEW) parameters, and is carried out by steps1312-1324. The data for profit maximization is preferably obtained fromthe entire sample production runs, and θ_(NEW) parameters are preferablychosen that will maximize profits (P) for the entire production runs.

[0390] Once the θ_(NEW) parameters are chosen, the process continues tostep 1326, at which a decision is made as to whether to continuescanning primary thresholding parameters (θ_(PRIME)), whose span is setby the user around the starting θ_(PRIME) in step 1302 with arestriction that θ_(PRIME) does not become tighter than the 1^(st) protothresholding. If a decision is made to continue θ_(PRIME) scanning, thenthe process continues to step 1328, where θ_(PRIME) is applied to the1^(st) PD file to generate a defect file labeled SD_(PRIME) file. Theparameters shown in FIG. 11 above must be defined for the profitmaximization process for the primary test recipe. Since only the pixelscommonly reported as defects in DF_(PRIME) and DF_(NEW) were reviewed bythe operator of the TFT-array repair equipment, and the operatorattempted to repair the pixels when the defects were visually confirmed,the table of FIG. 8 needs to be used for the defect sorting table forthe assumed scenario of primary-test-only at the TFT-array test stage202. By comparing the table of FIG. 8 and FIG. 11, one can obtain therevised defect sorting table in conjunction with the initial defectsorting of FIG. 11, for the assumed scenario of primary-test-only. Thistable is shown in FIG. 16.

[0391] The table of FIG. 16 is used in step 1330, to obtain theparameters of FIG. 11. The expressions for CPD, MPD, CND, and MND areobtained as follows:

CPD(UGc+UUc)∩PD _(PRIME)=(UGc+UUc)∩(1^(st) PD file ∩SD _(PRIME));  (264)

MPD=(UGm+UUm)∩PD _(PRIME)=(UGm+UUm)∩(1^(st) PD file∩SD _(PRIME));  (265)

CND(UGc+UUc)−CPD; and  (266)

MND(UGm+UUm)−MPD.  (267)

[0392] Then, Equations (208) to (210) can be used to calculate theeffect of the primary-test-only.

[0393] At step 1332, for tuning of the primary test recipe, θ_(PRIME) isupdated and applied to the 1^(st) PD file to generate the SD′_(PRIME)file. The process then proceeds to step 1334 (FIG. 13D), where it isdetermined if θ_(PRIME) has been updated to tighter or looserthresholding. If θ_(PRIME) is updated to tighter thresholding, then theprocess proceeds to step 1338, where the values of CPD and MPD decreaseby ΔCPD and ΔMPD, respectively, and the value of SD increases by ΔSD,because the SD′_(PRIME) files report additional defects of ΔSD. Theexpressions for ΔCPD, ΔMPD, and ΔSD are obtained as follows usingEquations (264) and (265):

ΔCPD=CPD∩SD′ _(PRIME)=((UGc+UUc)∩PD _(PRIME))∩SD′ _(PRIME);  (268)

ΔMPD=MPD∩SD′PRIME=((UGm+UUm)∩PD _(PRIME))∩SD′ _(PRIME); and  (269)

ΔSD=SD′_(PRIME) −SD _(PRIME).  (270)

[0394] If θ_(PRIME) is updated to looser thresholding, then the processproceeds to step 1336, where the values of CSDrp, CSDnr, MSDrp, MSDnr,Well, and SD decrease by ΔCSDrp, ΔCSDnr, ΔMSDrp, ΔMSDnr, ΔWell, and ΔSD,respectively, because the SD′_(PRIME) files do not report these asdefects. The expressions for ΔCSDrp, ΔCSDnr, ΔMSDrp, ΔMSDnr, ΔWell, andΔSD are obtained as follows using the table of FIG. 16:

ΔCSDrp=CSDrp∩PD′ _(PRIME) =GGcr∩PD′ _(PRIME)+(1−Nc)(GUc∩PD′_(PRIME));  (271)

ΔCSDnr=CSDnr∩PD′ _(PRIME) =GGc∩PD′ _(PRIME);  (272)

ΔMSDrp=MSDrp∩PD′_(PRIME) =GGmr∩PD′ _(PRIME)+(1−Nm)(GUm∩PD′PRIME);  (273)

ΔMSDnr=MSDnr∩PD′_(PRIME) =GGm∩PD′ _(PRIME);  (274)

ΔWell=Well∩PD′ _(PRIME) =GGr∩PD′ _(PRIME) +Nc(Guc∩PD′_(PRIME))+Nm(Gum∩PD′ _(PRIME)); and  (275)

ΔSD=SD _(PRIME) −SD′ _(PRIME),  (276)

[0395] where PD′_(PRIME)=1^(st) PD file∩{overscore (SD′_(PRIME))}.

[0396] Once the parameters are updated using Equations (268) to (270)for tighter θ_(PRIME) and using Equations (271) to (276) for looserθ_(PRIME), then the effect of the new θ_(PRIME) can be obtained by usingthe analysis of Section VIII. Therefore, profit maximization can beachieved by taking the maximum value of P while θ_(PRIME) is scannedthrough the starting θ_(PRIME) in its scanning zone. Once the profitmaximization has been achieved for one θ_(PRIME) parameter, then anotherprofit maximization process is performed for another θ_(PRIME) parameterin its scanning zone. This profit maximization process is repeated forall the remained θ_(PRIME) parameters, and is carried out by steps1332-1344. The data for profit maximization should be obtained from theentire sample production runs and θ_(PRIME) parameters are preferablychosen that maximize the profit (P) for the entire production runs. Theprocess then ends at step 1346.

[0397] X. Dependence of Thresholding Parameters on Defect Probability

[0398] As discussed in Section III, when measuring TFT-array panelsusing TFT-array test equipment, normal pixels have some voltagedistribution around a mean value, as shown in FIG. 3, mainly due to thenoise involved in measuring the pixel voltages. This causes some of thenormal pixels with extreme noise magnitudes to be falsely reported asdefects. The voltage distribution of defective pixels is not alwaysdistinct from that of normal pixels, and this causes some of thedefective pixels to go through the TFT-array test undetected and becomeunder-killed defects.

[0399] In general, tighter thresholding allows less under-killed defectsand more over-killed defects, and looser thresholding allows moreunder-killed defects and less over-killed defects. Some defects exhibitvery small defect signals, meaning that their pixel voltages are veryclose to normal pixel voltages, and very tight thresholding is requiredto detect these kinds of defects however, very tight thresholdingresults in too many over-killed defects. An improved thresholding schemewill now be described that detects more defects, but only increasesover-killed defects by a negligibly small amount.

[0400] If multiple pixels in very close proximity have some deviation intheir pixel voltages from the normal pixel voltage, then tighterthresholding than is needed for an isolated defect should be applied tothese pixels, because multiple defects in very close proximity are muchmore likely to come from a single process abnormality that coversmultiple pixels than from multiple isolated defects in close proximity,as will now be explained.

[0401] The probability of having the second isolated defect in the areaof A_(NEAR) near the first defect (PB_(NT)) is given by“PB_(NT)=A_(NEAR)/A_(TOTAL)”, where A_(TOTAL) is the total display areaof the TFT-array panel. The area covering two defects in close proximity(A_(NEAR)) is usually very small compared to A_(TOTAL). If A_(NEAR) isdefined by a 10 by 10 pixel array and A_(TOTAL) is 10⁶ pixels, thenPB_(NT)=10×10/10⁶=10⁻⁴.

[0402] If the probability of a single process abnormality covering twopixels is comparable to that of the first isolated defect, then theprobability of having two defects in very close proximity due to asingle process abnormality is larger (on the order of about 10⁴ larger)than that due to two isolated defects in close proximity. Therefore, thethresholding should be tighter for multiple defects in close proximityas the number of defects in close proximity increases, because theprobability of having multiple defects in very close proximity due to asingle process abnormality is increasingly larger on the order of about10⁴ times the number of multiple defects than that due to multipleisolated defects in close proximity.

[0403] Single process abnormalities involving a signal line, such asdata, scanning, or common line, can cause multiple defects along theline. The probability of having multiple isolated defects in a linearform is extremely low, based on reasoning similar to that explainedabove. Thus, the thresholding for defects in a line should also betighter than the normal thresholding used for an isolated defect.

[0404] Process abnormalities can effect a relatively large area of thedisplay, causing many isolated pixels over the relatively large area tohave pixel voltages that are slightly deviated from the mean value ofnormal pixel voltages. Thus, tighter thresholding than that normallyused for detecting an isolated defect should be applied to those defectsscattered over the relatively large area, if the total number of defectsin the defined area exceeds some pre-defined critical number. Ingeneral, tighter thresholding should be applied to multiple defects ifthey are caused by certain single process abnormalities with higherprobability.

[0405] In some manufacturing lines, additional inspection equipmentcalled automated optical inspection (AOI) equipment may also be used inthe TFT array process area to detect process abnormalities in theTFT-array panel. One of the difficulties of this type of inspection isthat not every process abnormality detected by the AOI equipment isrelated to functional defects in the TFT-LCD unit, even though theprocess abnormalities detected by AOI equipment end up causingfunctional defects with reasonably high probability. Thus tighterthresholding should be applied to the defects already detected asprocess abnormalities by the AOI equipment. One can correlate thethresholding of the TFT-array test with the area of process abnormalitydetected by the AOI equipment, so that tighter thresholding is used asthe area of process abnormality gets larger.

[0406] Therefore, in order to increase the defect detection efficiency,the first defect file should be generated by the tightest thresholdingto detect all the potential defects. Then, the defect file is preferablyscreened by next tightest thresholding to detect the defects thatsatisfy the right criteria for that specific thresholding. Thisprocedure is preferably continued until all the different thresholdinglevels are applied to the potential defects.

[0407] XI. Sample Results

[0408] As discussed above, the profit of TFT-LCD manufacturing can bemaximized by optimizing the parameters of the TFT-array test. The profitmaximization is performed by finding the test parameters that strike theright balance between improvement of cell and module yields, andreducing the costs of the TFT-array repair process.

[0409]FIG. 17 is a plot showing an example of the distribution of normal1700 and defective 1710A and 1710B pixel voltages of a TFT-array panel,which are used as the basis of parameter optimization. The distributionof normal pixel voltages 1700 can be represented by a statisticaldistribution function, because of the large number of pixels perTFT-array panel, and because of sensor's statistical measurementproperties. Thus, the distribution of normal pixel voltages 1700 can bewell represented by a normal distribution function. The distribution ofdefect pixel voltages 1710A and 1710B is not fixed, but is dependent onthe specific process problems. The distribution of defect pixel voltages1710A and 1710B is assumed to be constant between arbitrary values ofpixel voltages.

[0410] As discussed above, TFT-array test equipment uses thresholdingparameters to detect the defective pixels. Pixels are reported asdefects when their pixel voltages fall outside of the threshold region.If a normal pixel has its pixel voltage outside of the threshold region,then the normal pixel is wrongly reported as a defect and this kind ofpixel is called an over-killed defect. If a defective pixel has itspixel voltage within the threshold region, then the defective pixel iswrongly reported as a normal pixel, and this kind of pixel is called anunder-killed defect.

[0411]FIG. 18 is a plot showing the over-killed and under-killed defectsas the thresholding parameters are scanned, based on the distribution ofnormal and defect pixel voltages shown in FIG. 17.

[0412]FIG. 19 is a plot showing the differential effect of changingthreshold parameters for under-killed defects, as compared with theresults obtained with the primary thresholding parameters, based on theunder-killed defects shown in FIG. 18.

[0413]FIG. 20 is a plot showing the differential effect of changingthreshold parameters on over-killed defects, as compared with theresults obtained with the primary thresholding parameters, based on theover-killed defects shown in FIG. 18.

[0414]FIG. 21 is a plot showing the differential effect of changingthreshold parameters on cell and module yields, as compared with theresults obtained with the primary thresholding parameters, based on thedifferential under-killed defects shown in FIG. 19.

[0415]FIG. 22 is a plot showing the differential effect of changingthreshold parameters on total monetary benefit, as compared with theresults obtained with the primary thresholding parameters, based on thedifferential effect on over-killed defects shown in FIG. 20 and thedifferential effect on cell and module yields shown in FIG. 21.

[0416]FIG. 23 is a plot showing the under-killed defects for differentdefect density values. The numbers in the legend indicate themultiplication constants applied to the starting defect density used inFIG. 17.

[0417]FIG. 24 is a plot showing the differential effect of changingthreshold parameters on the total monetary benefit for the defectdensities used in FIG. 23. The numbers in the legend indicate themultiplication constants applied to the starting defect density used inFIG. 17. The profit maximization can be achieved by taking thethresholding parameters that yield the peak points of total monetarybenefit, while the thresholding variables are scanned around the primarythresholding parameters.

[0418]FIG. 25 is a plot showing how the profit improvement increaseswith increasing defect density, based on the differential total monetarybenefit shown in FIG. 24. The alphabets in the legend indicate thedifferent scanning zones used in FIG. 24.

[0419] The foregoing embodiments and advantages are merely exemplary andare not to be construed as limiting the present invention. The presentteaching can be readily applied to other types of apparatuses. Thedescription of the present invention is intended to be illustrative, andnot to limit the scope of the claims. Many alternatives, modifications,and variations will be apparent to those skilled in the art. In theclaims, means-plus-function clauses are intended to cover the structuresdescribed herein as performing the recited function and not onlystructural equivalents but also equivalent structures.

What is claimed is:
 1. A method of determining thresholding parametersfor a test recipe that will optimize a liquid crystal display (LCD)manufacturing parameter, wherein the test recipe comprises pixel drivingsignals applied to electrode array panels by an array test stage, andthe thresholding parameters are used by the array test stage to identifygood and defective pixels in the electrode array panels based on pixelvoltage distributions generated in response to the pixel drivingsignals, the method comprising: (a) evaluating the LCD manufacturingparameter using thresholding parameters with current values; (b)evaluating the LCD manufacturing parameter while scanning the value of athresholding parameter from its current value and holding the values ofother thresholding parameters, if any, at current values; (c)identifying a new value for the scanned thresholding parameter thatresults in an optimized LCD manufacturing parameter, based on step (b);and (d) repeating steps (a)-(c) until all thresholding parameters havebeen scanned from their current values.
 2. The method of claim 1,wherein the test recipe generates positive polarity and negativepolarity pixel voltage distributions.
 3. The method of claim 2, whereinthe pixel voltage distributions generated by the pixel driving signalscomprise: a positive polarity normal pixel voltage distribution; apositive polarity defective pixel voltage distribution; a negativepolarity normal pixel voltage distribution; and a negative polaritydefective pixel voltage distribution.
 4. The method of claim 3, whereintwo thresholding parameters are used by the array test stage for each ofthe pixel voltage distributions.
 5. The method of claim 1, wherein theevaluation of the LCD manufacturing parameter is based on under-killedand over-killed defect parameters.
 6. The method of claim 1, wherein theLCD manufacturing parameter comprises an LCD yield.
 7. The method ofclaim 1, wherein the LCD manufacturing parameter comprises profit.
 8. Asystem for determining thresholding parameters for a test recipe thatwill optimize a liquid crystal display (LCD) manufacturing parameter,wherein the test recipe comprises pixel driving signals applied toelectrode array panels, comprising: an array test stage for applying thetest recipe to the electrode array panels, and for identifying good anddefective pixels in the electrode array panels based on the thresholdingparameters and the pixel voltage distributions generated in response tothe pixel driving signals; and a processor for: (a) evaluating the LCDmanufacturing parameter using thresholding parameters with currentvalues; (b) evaluating the LCD manufacturing parameter while scanningthe value of a thresholding parameter from its current value and holdingthe values of other thresholding parameters, if any, at current values;(c) identifying a new value for the scanned thresholding parameter thatresults in an optimized LCD manufacturing parameter, based on step (b);and (d) repeating steps (a)-(c) until all thresholding parameters havebeen scanned from their current values.
 9. The system of claim 8,wherein the test recipe generates positive polarity and negativepolarity pixel voltage distributions.
 10. The system of claim 9, whereinthe pixel voltage distributions generated by the pixel driving signalscomprise: a positive polarity normal pixel voltage distribution; apositive polarity defective pixel voltage distribution; a negativepolarity normal pixel voltage distribution; and a negative polaritydefective pixel voltage distribution.
 11. The system of claim 10,wherein two thresholding parameters are used by the array test stage foreach of the pixel voltage distributions.
 12. The system of claim 8,wherein the evaluation of the LCD manufacturing parameter is based onunder-killed and over-killed defect parameters.
 13. The system of claim8, wherein the LCD manufacturing parameter comprises an LCD yield. 14.The system of claim 8, wherein the LCD manufacturing parameter comprisesprofit.
 15. An article of manufacture, comprising: a computer usablemedium having computer readable program code embodied therein fordetermining thresholding parameters for a test recipe that will optimizea liquid crystal display (LCD) manufacturing parameter, wherein the testrecipe comprises pixel driving signals applied to electrode array panelsby an array test stage, and the thresholding parameters are used by thearray test stage to identify good and defective pixels in the electrodearray panels based on pixel voltage distributions generated in responseto the pixel driving signals, the computer readable program code in thearticle of manufacture causing a computer to: (a) evaluate the LCDmanufacturing parameter using thresholding parameters with currentvalues; (b) evaluate the LCD manufacturing parameter while scanning thevalue of a thresholding parameter from its current value and holding thevalues of other thresholding parameters, if any, at current values; and(c) identify a new value for the scanned thresholding parameter thatresults in an optimized LCD manufacturing parameter, based on step (b);and (d) repeat steps (a)-(c) until all thresholding parameters have beenscanned from their current values.
 16. The article of manufacture ofclaim 15, wherein the computer readable program code causes a computerto evaluate the LCD manufacturing parameter based on under-killed andover-killed defect parameters.
 17. A program storage device readable bya machine, tangibly embodying a program of instructions executable bythe machine to perform method steps for determining thresholdingparameters for a test recipe that will optimize a liquid crystal display(LCD) manufacturing parameter, wherein the test recipe comprises pixeldriving signals applied to electrode array panels by an array teststage, and the thresholding parameters are used by the array test stageto identify good and defective pixels in the electrode array panelsbased on pixel voltage distributions generated in response to the pixeldriving signals, the method comprising: (a) evaluating the LCDmanufacturing parameter using thresholding parameters with currentvalues; (b) evaluating the LCD manufacturing parameter while scanningthe value of a thresholding parameter from its current value and holdingthe values of other thresholding parameters, if any, at current values;(c) identifying a new value for the scanned thresholding parameter thatresults in an optimized LCD manufacturing parameter, based on step (b));and (d) repeating steps (a)-(c) until all thresholding parameters havebeen scanned from their current values.
 18. The program storage deviceof claim 17, wherein the test recipe generates positive polarity andnegative polarity pixel voltage distributions.
 19. The program storagedevice of claim 18, wherein the pixel voltage distributions generated bythe pixel driving signals comprise: a positive polarity normal pixelvoltage distribution; a positive polarity defective pixel voltagedistribution; a negative polarity normal pixel voltage distribution; anda negative polarity defective pixel voltage distribution.
 20. Theprogram storage device of claim 19, wherein two thresholding parametersare used by the array test stage for each of the pixel voltagedistributions.
 21. The program storage device of claim 17, wherein theevaluation of the LCD manufacturing parameter is based on under-killedand over-killed defect parameters.
 22. The program storage device ofclaim 17, wherein the LCD manufacturing parameter comprises an LCDyield.
 23. The program storage device of claim 17, wherein the LCDmanufacturing parameter comprises profit.